Evaluate F. dr where F = (0, -3y, 3x), and C' is given by F(t) = (t, sin(t), cos(t)), 0

Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

A:

Q: 6. If f(r, y) = tan-(x/y), then the value of f,(3, 2) is %3D -3 (b) (c) 1 (d) -2 (a) 13

A:

Q: Find f if ƒ"(t) = 2et + 3 sin(t), ƒ(0) = 2, ƒ(π) = 5. f(t) =

A: f''( t ) = 2et + 3sint f( 0 ) = 2 f( π ) = 5

Q: Find f. f(0) = = f"(0) = sin(0) + cos(8), f(0) = 3, f'(0) = 2

A: f"θ=sinθ+cosθ Integrating both sides  ∫f" θdθ=∫sinθdθ+∫cosθdθ f'θ=-cosθ+sinθ+C..... (i)  Put θ=0…

Q: Let f(1) = 8 sin z +5 cos z %3D f'(z) = %3D

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Q: Let (t) = Find '(t) '(t)=<

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Q: Find the derivatives of each of the following functions f(x)=-2 sinx b) y=-cos²x c) y = 3x sin x d)…

A: find the dervative

Q: Let f(z) = 4 cos I-3 tan z. %3D S(2) =D %3D

A:

Q: Let h(t) = tan(3t + 8). Then h'(5) is and h"(5) is

A: As we know that the chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1   Given: ht=tan3t+8 Now…

Q: (a) Differentiate f(x) = Vx+4 by using the first principle. (b) Differentiate the following…

A:

Q: 2. Find the derivative (dy/dx) of the following functions: n) y = 1- cos 3x sin 2x + sin 8x tan 4x

A: 2) n) It is required to find the derivative of the function y=1-cos3xsin2x+sin8xtan4x.

Q: Find F as a function of x and evaluate it at x = 0, x = /3, and x = = Tt/2. F(x) 6 de

A: We will use basic formula of Integration for first one and from second part just Value of the…

Q: of of +y y Let f(x, y) = x$y² tan Then x equals X

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Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: Let f (t) = te* +e sin 10t. Find L{f (t)}.

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Q: The function f (x) = x sin is continuous on the interval (-1,1). O True O False

A:

Q: Find extrenhum of one of the following function 1. 2(a, y) = sin2(x- 0.5) + artg (y- 0.5) rE (-1,1],…

A: Let us find the Extremum of the given function in the next steps.

Q: Find f. f(t) =|| f"(t) - 3et+ 5 sin t, f(0) = 0, f(T) = 0

A: To find f.f''t=3et+5 sin t, f0=0, fπ=0

Q: f(x.y) = xtan(). =tan( ес

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Q: It is given that f(x) = tan (1 +x). %3D Find f(0) and f '(0), and show that f "(0) = -

A: We know thatddxtan-1x=11+x2

Q: Vリ What is F'(;) 4 ? 16 π 4 π ミ|N

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Q: x+y %3D 21. Prove that tan-x + tan-'y tan - xy.

A: Using tan(A+B) =( tan(A) + tan(B) )/(1- tan(A) tan(B) ).

Q: one of the following pairs of functions are orthogonal on interval [-1, 1] Select one: x.cosx b. x,X…

A: Given the interval [-π,π] and the pair of function. a. x2,cosxb. x,x c. sinx,xd. NOTe. sinx,cosx We…

Q: Let f"(t) = 2t + sin t, f(0) = 1 and f'(0) = 2. Evaluate f(27).

A: