Evaluate F· dī where C F = = < 3z, 2y, – 4x > , and C is given by - T(t) = < t, sin(t), cos(t) > , 0 < t < T 0

Q: Let c>0 be a constant.  Is this result true or false?

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Q: = F(x) = In t dt, what is F'(x)? (Do not include "F' (x) =" in your answer.) %3D 3+ 12

A: F(x)=∫0x5ln t3+t2dtF'(x)=ddx∫0x5ln t3+t2dtLet u=x5So,F'(x)=ddx∫0x5ln t3+t2dt⇒F'(x)=ddx∫0uln…

Q: Find f'(x) and f'(c). Function Value of c f(x) = sin x f'(x) : f'(c) =

A: Given function

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Q: e function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant

A: The given function is f(x,y)=x-12+y-12 and subjects to the constraint x2+y2=8 the formula for the…

Q: f(z) is a twice differentiable function with f(0) = 1, f(2) = 4, f'(2) = 5, Then af"(x)dx = %3D

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Q: Q:f(x)={xe X = 0 X = 0 test f(x) is continuous at x = 0

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Q: F F) s an antiderivative of x-+x-, then what is the value of F(1)-F(-1)2 -1

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Q: f (x) = | ef(t) + e² dx then f(x) is equal to ee -1+1 2ee-1 O 4. seçenek O 1. seçenek 2ee -1 +1 2ee…

A: We have the following function given as such: f(x)=∫0xetf(t) +exdx So we will evaluate for this…

Q: – x®y³, 6. Given f(x, y) = e®° - show that fxy = fyx.

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Q: a. Find the antiderivative of f(x) = -25x e F(x) = %3D

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Q: Find the antiderivative F(x) of function F (x) = 3 such that F(1)=0. r4

A: Anti derivative: ∫F(x)dx = f(x)

Q: Let F(x) be an antiderivative of f(x), with F(1) = 30 and | f(x) dx = -8. What is F(6)?

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Q: Given: f(x, y) = arctan Find: F ƒ(x, y) dxdy x² - y² (x² + y²)² 3²-x² (x² + y²)² -y³ (y³ + xy²)² y²…

A: Given: fx, y=arctanxyTo Find: ∂2fx, y∂x∂y

Q: Let f(x) = 4x - 8x. Find F(x), the antiderivative function, if F(1) = 3.

A: Let f(x)=4x2-8xTo find the antiderivative function F(x)if F(1)=3

Q: Find the linearization of the function y = f(x) = x2 sin(x) at a = π/4 and use it to approximate the…

A: Given,

Q: Find a function f and a real number a such that 4 : | f(t) dt = x tan- x.

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Q: Let F(x) be an antiderivative of f(x). If F(1) = 12 and f (x) dx = 17, what is F(4)?

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Q: nf (x) = 1 – | f(t) dt eşitliğinden f(x)

A: Given πf(x)=1-∫0xf(t)dt                   (1) We have to find f(x)

Q: (c) A non-constant function f : [0, 1] → R such that f(x) > 0 for any r e [0, 1] but | f(x)dx = 0.…

A: Let us consider a function f:0,1→ℝ such that fx≥0 for all  x∈0,1.  Suppose fxn be a sequence of…

Q: ind the linearization of the function given below at the specified point. f(x) = 5 In(x) at a = 1…

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Q: (c) A non-constant function f : [0, 1] →R such that f(x) > 0 for any r € [0, 1] but | f(x)dx = 0.…

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Q: a) Consider f (x) = x³. Write the linear approximation of f for x near 2. Let's call this linear…

A: According to Bartley guidelines first question done....for remaining questions you have…

Q: 8. Find the value of a if F = (axy-z)i+(x+2 yz) j+(y - axz)k is irrotational. %3D

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Q: the guotient f(xth) f(a) where h is cortont.

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Q: 5. Given F(x) = cos (t) dt, determine F'(x). 2

A: Using leibniz rule  Explanation is given below....

Q: . A function f(x) has the following properties: (=) de = 4, f(2)dz = 6, f(2)dz S r(2) dz = -2, […

A: a) We divide the integral into three subintegrals

Q: Find f'(x) and f'(c). f'(x) = f'(c) = Function f(x) = x cos(x) Value of c C= I 3

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Q: (f) f(x1,x2) = xî xª, where 0 < a<1, on R?+.

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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: lim f(k+h)+f(k) h→0 ds Q3) Using the definition calculate the derivatives h dk 1 S= k – k of the…

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Q: Find f'(x) and f'(c). Function SILJ f(x) = sin x X Value of c C = T Im 3

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Q: (a) Let f(z) = sin*(z). Find f' (x), T(2) = (b) Let f(x) = J (x) = sin(z³). Find f'(x). %3D

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Q: 6 X, 一T Sx< 0, 10, f(x) = %3D f(x+27) = f(x) 0 <x < T;

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the zeYo k its ovdev for Sunction f2)=1-Ti + Z+ e.

A: Given the function, f(z)=1-πi+z+ez. Now, in order to find the zero of the function f(z), we will…

Q: | f(x)dx < Suppose that f(x) < g(x) on [a, b]. By the Comparison Theorem, Is it also true that f'(x)…

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Q: 25. The function g(x) = [", |u| du is not differentiable at x = 0.

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Q: Consider the function f(x) = Let F(x) be the antiderivative Then F(x)= - 8 2 x³ x6 - 4 of f(x) with…

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Q: The function f(z)=e^(-y) sin⁡x is analytic function

A: Here, f(x,y)=e-ysin x          =e-ysin x+i(0) So, let u=e-ysin x, v=0 Now, ux=e-ycos x and vy=0 So,…

Q: f(x) is a twice differentiable function with f(0) = 4, ƒ(1) = 3, f'(1) = 6, Then So 3xf" (x)dx =

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Q: Consider the function f(x) = 2æ³ – 6x² + 8x – 9. An antiderivative of f(x) is F(x)= Aæ4 – Bæ³ + Cx²…

A: The given function is : f(x)=2x3-6x2+8x-9         The antiderivative of fx is the value of integral…

Q: Let F(x) be an antiderivative of f(x), with F(1) = 20 and * f (x)dx = -7. What is F(4)?

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Q: 2. Let f(x,y)= xe" and find a) fu. fy» fy

A: Please refer the attached image for complete solution.

Q: Differentiate f(x) = ax? with respect to x. Assume that a and k are positive constants. k+x f'(x) =…

A: f(x)=ax2k+x We need to find the derivative of the given function.

Q: g(x)dx = 12, 18, g(x)dx = 7, and iven f(x)dx %3D f(x)dx = 10 4f (x)dx Evaluate

A: Given function∫-17gxdx=12......1∫-17fxdx=18......2∫-13gxdx=7......3∫-14fxdx=10......4 We have to…

Q: Using the Fundamental Theorems of Calculus, find the second derivatives of F(x): esin t b. F(x) =…

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Q: Find the antiderivative F(x) of f(x) = 8(sec x)(sec x – 4 tan x).

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Q: 3 Let f(x) = V1- a? 1 – x2 Enter an antiderivative of f(x).

A: Solving the problem by the process of indefinite integral.

Q: (3) If | f(x) dx exists and c is a real constant, prove that f(2) dz = / f(x + c) dz. | {(x+c) Vel

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

Q: 2R then the constants R TCX If f(x) Rsin .2 S,f' and f(x)dx and S are respectively.

A: Introduction :Here we have asked to find the value of R and S

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.