• The domain of f(x) 3-х is 1-x2 1. R 2. R/{1,-1} 3. R/{3} 4. (0, co)

Q: The maximum value of F in F(x) = - 4 cos x is 2 4 1

A: We know range of cosine function is [-1,1] Therefore maximum value of f(x)= -4cosx is, f(x)=-4cosx…

Q: 22. The function f(x) = Vx – 6 is transformed according to (x, y) → (7x – 7, - y+1). the transformed…

A: Substitute fx for y in the transformation and simplify. x,y=x,f(x)→7x-7,-f(x)+1=7x-7,-x-6+1

Q: 5. Find the absolute extrema of f(x) = x’ + 3x – 9x + 4 on the closed interval [-4, 0].

A: The given function fx=x3+3x2-9x+4

Q: Find aa and bb so that the function f(x)={4x^3-3x^2+5, x<-2         {ax+b,             x is…

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Q: Find the absolute maximum and minimum values of the function f(x)-cos²x-3sinx on the interval 0≤x≤7.

A: First I have find the derivative of the given function and set them to zero .Solved them to get the…

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: Prove that = va² – x* if y =(f)sin~+ () + (9)v&* - x²

A: Differentiation wrt x

Q: The function f(x) 2x 36x + 162I - 7 has two critical numbers. The smaller one is x = and the larger…

A: The critical number of a function f is a number c such that either f'(c) =0 or f'(c) doesn't exist.

Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

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Q: Find f'(x). f(x) = O O O 6x - sin² (5x) f'(x) = O f'(x) = f'(x) = f'(x) = = 6-10sin(5x)cos(5x) 2√6x…

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Q: The range of F (x) = 3 sin 2 x is -3≤F(x)≤3 -1≤F(x)≤1 -2≤F(x)≤2

A: The given function is: F(x)=3 sin(2x)

Q: 23:- Find and sketch the domain of the following equations:- 1) f(x,y) = Ln(1 – x² – y²) (2)f(x, y)…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The function f(x)=2x^3−36x^2+162x−9 has two critical numbers. The smaller one is x = and the…

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Q: 7 Determine a value for r so that h(x) x + rx² – 7x has an inflection point at x = 5. 2 -- |

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Q: 22. (a) Find the critical numbers of f(x) = x*(x – 1)°. (b) What does the Second Derivative Test…

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Q: Find all critical numbers in the function f(x)=7 + 3^1/3 - 2sinX on the interval 0 < x < 2π

A: Critical number

Q: )=x+- at x = C at x = 0

A:

Q: 1. Find the maximum and the minimum values of the function f(x)= 2x – tanx %3D in the interval 3' 3

A: Given: f(x)=2x-tanx Differentiate the function with respect to x. f'(x)=ddx(2x-tanx)=2-sec2x…

Q: f(6) = 2sece+ tan@ 6 <8<8| %3D 7. Find all critical numbers of of the function

A: We have to find critical numbers for given function:

Q: Find the interpolating polynomial of degree two for f(x) cos(r2) +r on the interval [-1, 1] using…

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Q: for x 2 - X Is differentiable at x = 2 but not at x = 1.

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Q: 2. Find and classify all the critical points of f (x, y) = 7x – 8y + 2xy – x² + y³. %3D (1

A: Given: 2.Let us consider the given curve equation, fx,y=7x-8y+2xy-x2+y3 -----1

Q: . (a) Find the critical numbers of . f (x) = x 4 (x -1 )3(b) What does the Second Derivative Test…

A: (a) We say that x=c is a critical point of the function fx if fc exists and if either of the…

Q: . Find and classify all the critical points of f (x, y) = 7x – 8y + 2xy – x² + y³.

A: (2)  Given data curve is  f(x,y)=7x-8y+2xy-x2+y3.............(1) then fx=7+2y-2x    &amp;…

Q: Find all the critical points for the function f(x, y) = x² + 8xy + 4y² +3. (Use symbolic notation…

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Q: 4.x +1 1 with f'(x) = 1/ 56x2 - 156x + 115 14x – 19 - - 3. Let f(r) = and f"(x) 4 %3D 3 5 Vr2 – 3x +…

A: To find the points on which it is concave up or concave down

Q: The antiderivative of the function 4 + 10x is. x2 f(æ) = 4 + 5.0x2 + c - -4 5.0x2 + c -10 + 2.0x2 +…

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Q: 6. Obtain the TSE of f(x)=2x-² in powers of (x-1).

A: Solution is here

Q: 1. Find all the critical numbers of the function (Justify Your Answer) (a) [5Vx – 2 f(x) = x > 2…

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Q: Find the maximum value of f(x)=2sin(x)cos(x).

A: Given: f(x)=2sinxcosx The above function can be written as: f(x)=sin2x…

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: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Given function:                         y=ex-e-x The domain of a function is the set of input values…

Q: ∇⋅F of F = (2x3y)i-(3y2z)j+(xz3)k at (1,2,-1). a. 27 b. -34 c. 4 d. -7

A: The del operator is used to represent the partial derivatives with respect to the variables defined…

Q: 7 For the function eX, the linear approximation around x = 2 is %3D

A:

Q: x = -1 is a critical number for g(x) = xª +x³ +x - 1. But the second derivative test fails for x =…

A: Explanation of the answer is as follows

Q: 1. Id f (u) = - sec u, find f '(u)

A: According to our guideline, we are supposed to install only the first question if you want any…

Q: 2 f(x, y) = x² + 3xy

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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: The function f(x) : (2х — 6)е has one critical number. Find it. - x =

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Q: 2 Integrate the function f(2) = (z - 10i) from z = 0 to z = 5 + 5i along the line x = y.

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Q: Find the critical numbers of the function  f(x) = 2cos x + sin 2  x

A: Since, we have been given that f(x)= 2 cos(x) +sin2 (x) -(i)Our Aim is to find the critical numbers…

Q: 1. f(x) = Vx - 1 at x = 5 %3D 2. f (x) = at x = 2 x-2

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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 ý of the function x2 - e2x+3y - In(xy) = 0. %3D

A: Consider x2-e2x+3y-ln(xy3)=0We differentiate it implicity, we…

Q: he function f(x)=2x^3−36x^2+162^x−7 has two critical numbers. The smaller one is x=    and the…

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Q: 8. x' + 10x² + 6x + 4 is concave down. 3 Determine the interval(s) at which f(x) = -- a) O(-1, 00)…

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Q: 1. f(x) = x2 + x – 1 for all values of x %3D

A: A detailed solution is given below

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.