Find the constant a such that the function sin x -13 - S(x) = %3D a+ 11x, x 20 is continuous on the entire real line.

Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

Q: Find the domain of the function. f(x) = ln ( 1/ (x + 1)

A: f(x)=ln1x+1

Q: then find f(x). | f(x)dx = = ln([x]) In(x) - sec(x) - 4e + 2 -x + 6x + C

A: The integration of f(x) equal to the;  ln(|x|)-sec(x)/3 -4ex/4+x2/2 +6x +C.

Q: d) Find the value of the constants ´ a ' and “ b ` that makes the function continuous at x=3 ; x3

A: f(x) is continuous at x = k if

Q: Find the intervals on which the function y=xx(x>0) is increasing and decreasing.

A: We take ln on both sides of the function

Q: Let f(x) = log2 (4x-x²)+2x. At what point is the tangent to the curve y = f(x) perpendicular to the…

A:

Q: Find the MacLaurin polynomial of degree 7 for the function sin (ot) dt. F(X) = %3D

A:

Q: Find the domain of the function. f(x) = ln(x^2 + 1)

A: Definition used:The domain of a function is the complete set of possible values of the independent…

Q: Find the value of constant K that makes the function below continuous at x = 2. -2x X < 2 X-2 f(x)…

A: Given,           fx=x2-2xx-2 ; x&lt;2kx-3 ; x≥2

Q: Find the derivative of f(x) =log,14-7x| 1 O a. f'(x) = (4-7x) In2 -7 Ob fl(x)= f'(x)=- (4-7x) In2 -1…

A: f(x) = log2 |4 - 7x| We are required to find the derivative of f(x).

Q: - 3x + 1, x S 4 Find the value k , if the function ƒ (x) = is continuous at x = 4. -kx + 1, x > 4

A: We will find the value of k as following.

Q: Find the third Taylor's polynomial f(x) = x3 – x² + 3x + 1 which can easily find the derivative at…

A:

Q: Зх-1 -dx 2 x+1

A: Given query is to find the integral.

Q: The function f(x) = 1 + x decreases to 1 as x- 0. Does f(x) dx exist?

A: Given function is f(x)=1+x-1f(x)=1+1x Given integral is evaluated as follows.…

Q: Find an analystic function whose real part is e-x (x sin y-y cos y)

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Q: Find the second derivative. 1 h(x) = x2 %3D | h"(x) = %3D

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Q: The function fis increasing on the interval (s) (A) 0 1 © x>2 D x 2

A:

Q: Find the linear approximation of the function below at r = -1 and use it to approximate f(-0.8). -7x…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: d) Find the value of the constants ' a’ and b ’ that makes the function continuous at x= 3 ах + b ;…

A:

Q: Find the absolute extrema of h(x)=3x÷2 on {-2,3}.

A: H(x) is the straight line so absolute extrema will be at ends on domain

Q: a) Let 3x2-1, for x3 f(x)= be a piecewise function. Eevaluate | Fx)dx= b) Let f(x) = 3x-1, for x< 3

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Q: Find the inflection points of the function f(x) = ln(x^2 + 1)

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Q: What is the derivative of the function f(x)= In(3x2) ? а. f'(x)= 2 b. None of these. с. 1 f'(x)= %3D…

A: We have given that  The function is f(x) = ln(3x2)

Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the average rate of change of the function f(x) = - 2x – 7x + 8, over the interval [-1,1]. -…

A:

Q: Find the domain of the function: h(x) = ln x2

A: h(x)=ln x2

Q: Evaluate the function: S de x(x-2) -dx (x–1)³

A:

Q: Find the domain of the function: f(x) = ln(4 - x)

A: we have to find the domain of the given function. f(x)=ln(4-x)

Q: Find The Domain of the Function. y = sin(log, x²]

A:

Q: 2. Find the derivative of each function a) f(x) = x³e/x et3+7 b) g(t) %3D t2 )듬x리 In(2x + 1) 8x+9 x3

A: According to our guidelines we can only answer 3 subparts of a question, rest you can repost

Q: Find the given higher-order derivative. 1. f'(x) = 5x? f''(x) = 2. f''(x) = 5 – - f"(#) = 3. f'(x) =…

A: Note: As per company guidelines we are supposed to solve only 1 question or 3 subaprts. So, kindly…

Q: Find the derivative of the function f (x) = /e* – In(x) 12 – 1/x) O (ex12 – 1) O (e2 – 1/x) e? -x)

A:

Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

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Q: Find d2y/dx2 by implicit differentiation: a. x3 + y3 = 1 b. y2 = 1 -2/x.

A: a. Given,

Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: find the value of the constant (a, b, or c) that makes the function continuous

A:

Q: Find f(2x)dx if f(x)dx = 1. Enter the exact answer. f(2x)dx

A:

Q: Find the interval on which f(x) =x'e is increasing.

A: We find f'(x) using the product rule

Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

Q: Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a =…

A:

Q: Given the function f(x) = x° – 4x² + 5x, find the open interval(s) where %3D f is concave down, i.e.…

A: Given the function f(x)=x3-4x2+5x, then we have to find the open interval where the function f is…

Q: The function f(x)=|x|·sin(x) is differentiable at x=0.

A:

Q: Use the sign pattern for the derivative dƒ/ dx = 6(x - 1)(x - 2)^2(x - 3)^3(x - 4)^4 to identify the…

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Q: 4) /() =2-2 3. 5) y = x*+2x+1 6.) f(x) =

A:

Q: Find the derivative F'(x) F(x) = (t? - 2t + 3)dt 1. -t2 +3t +c 3 О x2-2х +3 O x2 - 2x +5

A:

Q: Find the derivative. COSx a) f(x) = In %3D x2-4 4 b) g(x) = Vx + e2x + Tt

A: Given : (a) f(x)=ln(cosxx2−4)

Q: Find the first and second derivatives of the function. 14. f(x)= x to the 7/2+x to the 5/3-x to the…

A:

Q: Find the derivative f'(x) for the function f(x) = x² + x – 17. - O A. f'(x) = 2x – 16 В. f («) — 2а…

A: Find the derivative of f(x)

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;