Edited by asinus #2 3 I think they cancel each other out and the answer is just 10 Looking at it a little more formally I think it means \ (10= (x1)^3\\ \sqrt 3 {10}1=x\\ f (\sqrt 3 {10}1)= (\sqrt 3 {10}11)^3=10\) MelodyDomain of f(x) = x/(x^21) Natural Language;Knowledgebase, relied on by millions of students &

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Misc 7 Find the intervals in which the function f given by f (x) = x3 1/𝑥^3 , 𝑥 ≠ 0 is (i) increasing (ii) decreasing f(𝑥) = 𝑥3 1/𝑥3 Finding f'(𝒙) f'(𝑥) = 𝑑/𝑑𝑥 (𝑥^3𝑥^(−3) )^ = 3𝑥2 (−3)^(−3 − 1) = 3𝑥2 – 3𝑥^(−4) = 3𝑥^2−3/𝑥^4 = 3(𝑥^2−1/𝑥^4 ) Putting f'(𝒙) = 0 3(𝑥^2−Next find the ycoordinates of these points on the graph of f(x) 6Given f(x) = x²Let f R → R be a function such that f (x) = x^3 x^2 f' (1) xf (2) f'''' (3), x ∈ R Then f (2) equals Sarthaks eConnect Largest Online Education Community Let f R → R be a function such that f (x) = x^3 x^2 f' (1) xf (2) f'''' (3), x ∈ R Then f (2) equals ← Prev Question Next Question →
(A) If g is continuous at x = 1, then fg is differentiable at x = 1Free functions calculator explore function domain, range, intercepts, extreme points and asymptotes stepbystep1 12 Radius of Convergence Radius of Convergence There are exactly three possibilities for a
3 Follow 1 A K Daya Sir, added an answer, on 14/2/14 A K Daya Sir answered this f (x) = { (3x)/ (1x)} 23x taking log on both sides log (fx) = (2 3x) log { (3x)/ (1x)} log (fx) = (2 3x) log (3x) log (1x) Now differentiate f' (x) /f (x) = (2 3x) 1/ (3x) 1/ (1 x)Extended Keyboard Examples Upload Random Compute answers using Wolfram's breakthrough technology &F'(x)=2x5 The derivative of a function is the instantaneous rate of change of the function at a given point But we have a function, so we want to find the rate of change throughout We have two ways of doing this, and I'll show you both ways Method 1 The Power Rule This method only works for polynomials (x^n) We have a saying that helps remember the power rule




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X23(x4−1) View solution steps Short Solution Steps f ( x ) = 3 x ^ { 2 } \frac { 3 } { x ^ { 2 } } f ( x) = 3 x 2 − x 2 3 To add or subtract expressions, expand them to make their denominators the same Multiply 3x^ {2} times \frac {x^ {2}} {x^ {2}}Hence, the domain is all real numbers except 1 and 3 Also written as D_f=(oo,1)uu(1,3)uu(3,oo) To Find the Range Step 1 say f(x)=y and rearrange the function as a quadratic equation y=x/(x^22x3) rarr y(x^22x3)=x rarr yx^22yx3yx= 0 rarr yx^2(2y1)x3y= 0 Step 2 We know from the quadratic formula, x=(bsqrt(b^24ac))/(2a) that the solutions of x are real when b^24ac>=0 So likewise, we say, (2y1)^2X_0 = 1 y = x 3/2 4x;



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For instance, when D is applied to the square function, x ↦ x 2, D outputs the doubling function x ↦ 2x, which we named f(x) This output function can then be evaluated to get f(1) = 2, f(2) = 4, and so on Higher derivatives Let f be a differentiable function, and let f ′ be its derivativeF (x 2) = f (x) (a) Sketch the graph of the given function for three periods (b) Find the Fourier series for the given function f (x) = 1 2 ∞ k = 1= X∞ k=0 (−x2)k = 1 1−(−x2) = 1 1x2, for x <




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Professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, musicF ( x ) = x ( 2 x ^ { 2 } 1 ) ^ { 2 } ( 4 x ^ { 3 } ) f(x)=x(2x2−1)2(4x3) To multiply powers of the same base, add their exponents Add 1 and 3 to get 4 To multiply powers of the same base, add their exponents Add 1and 3to get 4 x^{4}\left(2x^{2}1\right)^{2}\times 4 x4(2x2−1)2×4(1) Compute the length of the curve f(x) = x 3/2, for 0 x 4 (2) Compute the length of the curve f(x) =x 3 / 3 1 / 4x, for 1 x 2 (3) Compute the length of the curve f(x) = e x e x / 2, for 0 x 2 (4) Compute the surface area generated by revolving the curve f(x) = 2 , 1 x 4 about the xaxis



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Find the values of a and b so that the function f(x) = x a√2 sin x, 0 ≤ x ≤ pi/4 asked in Mathematics by Sanskar ( 339k points) continuity and differntiabilityTaking second derivative of f(x) we get, f ′ ′ (x) = 2 (1 2 x − 1) this shows that f(x) has a local maxima at x = − 3 1 and a local minima at x = 2 1 Which means in between 0 ≤ x ≤ 1 f(x) has a minima at 1/2 and f (x) = 1 at x = 0 and f (x) = 2 at x = 1, also f (x) = 1 / 4 at x = 1 / 2 As per question we have g (x) = Min f (t) 0X_0 = 0 The normal line to the curve y = f(x) at the with coordinates (x_0, f(x_0)) is the line per the tangent line at P In Exercises 32 through an equation for the normal line to the given the prescribed point



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Given, f(x) = (x 1) 3 (x 2) 2 On differentiating both sides wrt x, we get Now, we find intervals and check in which interval f(x) is strictly increasing and strictly decreasing1 Example 1 f(x) = x We'll find the derivative of the function f(x) = x1 To do this we will use the formula f (x) = lim f(x 0 0) Δx→0 Δx Graphically, we will be finding the slope of the tangent line at at an arbitrary point (x 0, 1 x 1 0) on the graph of y = x (The graph of y = x 1 is a hyperbola in the same way that the graph ofY = (x^2 2)(x Squareroot x) x_0 = 4 y = (x^2 3)(5 2x^3);




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Compute answers using Wolfram's breakthrough technology &Group 1 x 3 Group 2 x 4 4x 2 Pull out from each group separately Group 1 (x 3) • (1) Group 2 (x 2 4) • (x 2) Bad news !!We can see, 1,2,3 has same image 0 ∴ f is not oneone onto test Let y be an element in the codomain R, such that y = f (x) ⇒ y =(x−1)(x−2)(x−3) Since, y ∈ R and x ∈ R ∴ f is onto




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Justify your answer f (x) = ( (x − 2)/ (x − 3)) Check oneone f (x1) = ( (x1 − 2)/ (x1 − 3)) f (x2) = ( (x2 − 2)/ (x2 − 3)) Putting f (x1) = f (x2) ( (x1 − 2)/ (x1 − 3)) = ( (x2 − 2)/ (x2 − 3)) Rough Oneone Steps 1Solution Let x4 x3 2x2 x 1 = f(x) and x3 − 1 = g(x) From the division algorithm we first obtain f(x) = (x1)g(x) 2(x2 x1), and then the next step yields g(x) = (x− 1)(x2 x 1), so gcd(f(x),g(x)) = x2 x 1 Solving the first equation for the remainder shows that (x2 x1) = 1 2 f(x)− 1 2(x1)g(x) 23Misc 7 Let f, g R → R be defined, respectively by f(x) = x 1, g(x) = 2x – 3 Find f g, f – g and 𝑓/𝑔 f(x) = x 1, g(x) = 2x – 3 (f g) (x) = f(x




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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreDivide f2, the coefficient of the x term, by 2 to get \frac{f}{2}1 Then add the square of \frac{f}{2}1 to both sides of the equation This step makes the left hand side ofDavneet Singh is a graduate from Indian Institute of Technology, Kanpur He has been teaching from the past 10 years He provides courses for Maths and Science at Teachoo




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H)(2), and (h / g)(2) This exercise differs from the previous one in that I not only have to do the operations with the functions, but I also have to evaluate at a particular x valueSimple and best practice solution for F(x)=x3x^2 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, soKnowledgebase, relied on by millions of students &




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F x = x 2 g x, g 1 = 6 a n d g ' 1 = 3 ⇒ f ' x = 2 x g x x 2 g ' x ⇒ f ' 1 = 2 1 g 1 1 2 g ' 1 ⇒ f ' 1 = 2 1 6 1 3 = 12 3 = 15 ⇒ f ' 1 = 15 Hope this information will clear your doubts about topic If you have more doubts just ask here on the forum and our experts will try to help you out as soon as possible RegardsExamples 2 f(x) = X∞ k=0 (−1)kx2k = 1−x2 x4 −x6 F(x) r(x) = g(x) x q(x) f(x) { r(x)} = g(x) x q(x) Clearly , Right hand side is divisible by g(x) Therefore, Left hand side is also divisible by g(x)Thus, if we add r(x) to f(x), then the resulting polynomial is divisible by g(x) Let us now find the remainder when f(x) is divided by g(x) Hence, we should add r(x) = x 2 to f(x) so



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Ex 51, 7 Find all points of discontinuity of f, where f is defined by 𝑓(𝑥)={ (𝑥3, 𝑖𝑓 𝑥≤−3@ −2𝑥, 𝑖𝑓−3<𝑥<3@ 6𝑥2, 𝑖𝑓 𝑥≥3)┤ Since we need to find continuity at of the function We check continuity for different values of x When x <Let the function f R → R be defined by f(x) = x 3 – x 2 (x – 1) sin x and let g R → R be an arbitrary function Let fg R → R be the product function defined by (f g) (x) = f(x) g(x) Then which of the following statements is/are TRUE ?Given f (x) = 2x, g(x) = x 4, and h(x) = 5 – x 3, find (f g)(2), (h – g)(2), (f ×




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Professionals For math, science, nutrition, historyGiven the functions, f(x) = x2 2 and g(x) = 4x 1, perform the indicated operation When applicable, state the domain restriction g(f(x)) 4 x2 1 16 x2 3 4 x2 7 16 x2 8 x 3 Please help I thinks that it is 16 x2 3F ( x) = 3 x 2 1 The derivative of a polynomial is the sum of the derivatives of its terms The derivative of a constant term is 0 The derivative of ax^ {n} is nax^ {n1} The derivative of a polynomial is the sum of the derivatives of its terms The derivative of a constant term is 0 The derivative of a x n is n a x n − 1 2\times 3x^ {21}




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Given f(x) = 2x 3 and g(x) = –x 2 5, find (g o f)(1) When I work with function composition, I usually convert (f o g)(x) to the more intuitive f (g(x)) form This is not required, but I certainly find it helpful In this case, I get (g o f)(1) = g(f(1))Free PreAlgebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators stepbystepFactoring by pulling out fails The groups have no common factor and can not be added up to form a multiplication Polynomial Roots Calculator 44 Find roots (zeroes) of F(x) = x 4 4x 2 x 3



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1 f(x) = X∞ k=0 x2k1 3k = x 1 3 x3 1 9 x5 1 27 x7 If f (x) = sin x cos x 1 and g(x) = x^2 x, x ∈ R, then fog(x) at x = 0 is asked in Sets, Relations and Functions by Maahi01 ( 245k points) composition of functionX_0 = 1 y = 2x 1/3x 5;




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