x3, x<2 Let f(x) = Find the values of a and b so that f'(2) exists. ax2 +b, x22

Q: 1- f(x,y) = In(x² + y?) at (1,1)

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: Find constants c1 and c2 such that F(x) = c1x sin x + c2 cos x is an antiderivative of f (x) = x cos…

A: To find constant c1 and c2 such that Fx=c1 xsinx+c2cosx is an antiderivative of fx=x cosx. Solution:…

Q: Find the most general antiderivative of f(x) = -3x – 7xL7. Note: Any arbitrary constants used must…

A: Topic = Integration

Q: 3. Find , 9 for the functions: ax' ây sin(x³ + y* ) x* +y , (x,y) = (0,0) f (x.y) = .(x.y) = (0,0)

A: f(x,y)=sinx3+y3x2+y2, x,y≠(0,0)0, (x,y)=(0,0)

Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(e, 1) =

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Q: Suppose F(r, y) is a C' function such that F(0, 0) = 0. What conditions on F will guarantee that the…

A: Let us consider, F^(x,y)=F(F(x,y),y)  On applying the implicit function theorem , can get a solution…

Q: 5. By considering the derivative of the function f : [-1,-1] → R defined by f(x) = show that f-¹…

A: Concept: inverse function: An inverse function, sometimes known as an anti function, is a function…

Q: -4 Find the line 1. f(x) = x³ - 2. f(x) = cos 2 3. f(x)

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Q: у (4) %— Зх3 8 e x7

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Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: of of For the function f(x,y)% 9x2- 3y°-4, find and dx dy of II

A: While calculating the partial differentiation of a function with respect to X we consider the other…

Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

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Q: Given the function f(x) = (x-4)2 + (y-5)2 (i) Find the critical points.  (ii) Using the second…

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Q: Dicuss the contiunity of the function f (x,y) = ln  (x+y-1)

A: We know: 1) Polynomials are continuous everywhere. That is, at every point in real number 2) Sum of…

Q: 4. For the function f(x, y) = exp (ax + by) find the maximal possible value of the directional…

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Q: 3 f(x) dx = 4, find | xf(x*) dx. If f is continuous and

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Q: Q3: Use Chain Rule to differentiate the following functions 1. f(r) = (4x² - 3r + 2) 2 2. y = csc(4…

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Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: estion 9 Find the derivative of f(z) = 3z13 - 4+1. IDo? la sin (a) f' (x) =}

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Q: The function f(x) = −2x³+3x²+36x has two critical points, c₁ and c₂. Find them and use the second…

A: We need to find and classify critical points.

Q: Q:2. Use the first derivative test to find the intervals on which the function is f(x) = x4. which…

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Q: 6. f(x) dx = 2, find If f is continuous and xf(x2) dx.

A: given f is continuous and ∫09 f( n) dx = 2 we have to find ∫03 xf (x3) dx = ? we solve this by the…

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: given: f=x3y2-yx+lnx to find:fyyxxx

Q: -2? + 15z - 27 f(z) = 3z2 + 7z + 6 C, I= 3 What value of C would make f(x) continuous at z = 3?

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Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =

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Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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Q: V². Find the derivative of f(x) = In x² +1 %3D x(2r - 1)2

A: Derivative: f(x)=lnx2+1x(2x3-1)2ln(mn)=ln m-ln nln(x2+1)=12ln(x2+1)

Q: Find the local linear approximation of f(x)= at 2+ x xo = 2, where Ax = x – 2. NOTE: Enter the exact…

A: while finding out the local linear approximation of any function f(x), what we do is to determine…

Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

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Q: 3 Let f(x) = 8x° 1 df 15x - 5, x2 1.5. Find the value of dx at the point x= 2004 = f(7). %3D

A: Known fact: derivative of f-1x=1f' f-1x.

Q: Find the absolute extrema of the function f(x) = (x2 + 18)273 on the interval[-4,3]. Find the second…

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Q: Find all points where the function f(x) = |x|p with p > 0 is differentiable. How does your answer…

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Q: We are given that the derivative of f is f′(x)=3x2−12x−15 and that f(1)=81.   The absolute maximum…

A: We are given that the derivative of f is f′(x)=3x2−12x−15 and that f(1)=81.   The absolute maximum…

Q: The point (0, 0) is the critical point of the function f(x, y) = Select one: O True O False x²y 2 +…

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Q: a.) On the interval (-o, 0), f"() b.) On the interval (0, 0), f"(x) = Thus, c.) On the interval (-o,…

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Q: 2 The function f(x)= (x² – 1) ³ , is decreasing on the interval (- 00,-2)U (0,2) AO (-1,0) U (1, ∞ )…

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Q: (X),4 %3D (b) Compute the derivative of f(x). (g) 4 (x)J – (4 + x) 10xh + 5h“ – x + 8 8 + x – 2. (a)…

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Q: he tangent line to y= f(x) at (-7, -6) passes through the point (-9, -2). Compute the following.  a)…

A: GIVEN DATA : Equation y=fx                         Tangent of the y=fx at -7,-6 passes through the…

Q: (a) Find the derivative of y = f(x) =2x+1 using this definition f (x+h)-f(x) f'(x)= lim h (b) If x…

A: Differentiate above function with respect to x

Q: df Find dx by using chain rule if f = u =-1 , x=-1 u+1

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Q: The function f(x) = (8x – 1)e® has one critical number. Find it. 4x - x =

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Q: 3 xf(x2)dx df(x) dx = -9, find If f is continuous and 0

A: f(x) is continuous

Q: f: (Z, +) → (Z, +) where f(x) = 2x. f: (R, +) → (R*, .) where f(x) = 2*

A: We will use definition of isomorphism

Q: Find and sketch the domain of the function. f(x, y, z) = ln(64 − 4x2 − 16y2 − z2)

A: Given function is      f(x,y,z) = ln(64-4x2-16y2-z2) We have to find the domain of this function.

Q: Find f(3,4) for f (x, y) = In(x + /x² + y²). %3D

A: Given:- f(x, y) =ln(x+√(x2+y2))  To find:- fx(x, y) at (3, 4)

Q: Find constants c1 and c2 such that F(x) = c1xe -x + c2e -x is an antiderivative of f(x) = 3xe -x .

A: Given: Fx=C1xe-x+C2e-x  and fx=3xe-x

Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

Q: 2.r By considering the derivative of the function f: [-1,1] → R defined by f(x) = show r2 +1' that…

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Q: 4. Using the expression (x + Ax)² = x" + nx-Ax +n(n – 1)x"-²Ax² + + Ax" ... prove that if f = ax"…

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