sin i dt 48. Let F(x) = | Show that x3 F(x) = x - x5 x7 +... 3. 3! 5. 5! 7.7! Evaluate F(1) to three decimal places.

Q: 1. f(t) = cos*t – sin*t 5. f(x) = tan 2x 1-cot 2x 2. y= sec20 – tan²0 3. f(x) = sin(cos x) %3D 3 4.…

A: Here we have to find derivative of given questions.

Q: 8 sin x Find an antiderivative F(x) of the function f(x) such that F (0) = 1- 3 + cos r

A:

Q: 2. True or False. The dx [Arctan(tan x)] = 1 for all x in the domain. ans. True

A:

Q: 1 Bin x į sin x, 0sxsn, Prove that f (x) = + 2 2 · If f (x) = { 0. cos 2nx -- n=1 4n? - 1 1 Hence…

A:

Q: a) f(x) = 3x + 5; interval [1,2]; %3D W = 10 interval ; 11m- b) f(x) = sin x;` %3D W = -1 2' 2

A: To verify the IVT for the specified function f, the interval a, b, and the indicated value w.a…

Q: 5. Find the absolute maximum and minimum of f(x) = 3 cos x on the interval [0, 27).

A: 5) to get critical points f'(x)=0f'(x)=ddx(3cosx)=-3sin(x)=0…

Q: 1. Find the critical numbers of f(x) = 2 cos(r) + sin (x) %3D

A: Given: f(x)=2cosx+sin2x  A number is critical if it makes the derivative of the expression equal 0,…

Q: 9) Find all relative extrema in the interval (0, 2π) for y = x - cos x

A: Here we have to find the relative extrema.

Q: undetermint coedticients 11 ON-4y = G²-3) sin x

A: The given problem is to solve the given non homogeneous differential equation using method of…

Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

A:

Q: cot-1(t) Given F (x) = 1+sin=1(3x) 24 ot-1 . dt, evaluate F (0) and F '(0).

A: We have to find F(0) and F'(0).

Q: 1. F (x) = sin x+ 2cos x – 5 %3D 2. G(x) = 3e* – 7log;x – 2 * 3. H (x) = 4sec x + 5tanx 4. Z (x) =…

A: Since there are multiple questions. We will solve only the first three questions. If you want to…

Q: #2. Verify Clairaut's Theorem for the given function f (s, t)= In (st)-s* sin (6t) +st.

A:

Q: 7. Determine f(x) so that Scon cos(In°x)f(x) dx = sin(ln²x) + C 2 Inx (a) 2 In x (b) In x (c) (d) 2

A:

Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

A:

Q: 2. Let f(x)=3 cos 2x + sin²x. a) b) Show that f'(x) = -5 sin 2x. In the interval <x<³ Find the value…

A:

Q: sin(x³ + y* ) Q3. Find of for the functions: .(x.y) (0,0) x'+y f(x.y) = .(x.y) = (0,0)

A: f(x,y)=sin(x3+y2)x2+y2 uv'=vu'-uv'v2

Q: Given p(x)= sin2x+sinx on the domain [0,2pi]  a) Find the intervals on which p(x) is increasing an…

A:

Q: 9) f(x. v) = sin (x- 3y) Ans. f, =2sin(x-3y)cos(x-3y),. f, =-6sin(x - 3y)cos(x-3y)

A:

Q: 2. Let f(x) = 3 cos 2x + sinx. a) b) Show that f'(x) = -5 sin 2x. π 3π In the interval <x< one…

A: We need to find derivative and normal.

Q: (B) The evaluation of f- -dx is (x*+3x2 +1)[tan-( In|tan"+5| + e -In tan-( +c (i) (ii) (iii) None of…

A: No antiderivative could be found within the given time limit, or all supported integration methods…

Q: snip

A:

Q: Consider the graph of f (0) = sin(20) on the interval 0 <0 < 2n. What are the critical values of f ?…

A:

Q: (x²+y2 ) prove ne du + y ax -2 sin2u ( Euler's Rule) 5. If u = cot-1 that x ду x+y

A: We use the Euler's rule of partial differential in homogeneous function to solve this problem.

Q: Find the critical numbers of the function on the interval 0 < 0 < 2n. f(8) = 2cos(0) + sin?(0)…

A: Critical number

Q: 9. The value of f 1-x 1+x A. sin ¹¹x + √1 + B. sin¹x - √1 + dx x² + C x² + C C. sin ¹¹x + √1- x² + C…

A:

Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

A:

Q: sin(t) (F(x³)). dx Suppose F(x) dt. Use the Fundamental of Theorem of OCalculus to calculate 6+t

A: SOLUTION-

Q: sin 7Z „Find the residue of f (z)at z = 4 (z – 4)? Let f (z) =

A: Note:

Q: II. Let F(x) = | cos(3t – 1) dt. - sin 1. Find F(0). 2. Find F'(x x).

A:

Q: None c) cosh x + C sinh x +C 2 sinh x +C cosh x +C

A: The given integral,      12∫ex-e-xdx

Q: III. Let f(x) = 2 sin x 1. Use the local linear approximation of f at x = 0 to approximate e2…

A: Given problem:-

Q: 2. Let f(x) = -x³ - cosx and po = -1. Use Newton's method to find p2. Could po = 0 be used?

A:

Q: Find f. f"(x) = cos(x), f(0) = 1, f'(0) = 8, f"(0) = 6 f(x) = sin x + 7x/2 + 7x +8|

A: We will first find the general solution of f"'(x)=cos(x)

Q: 1+ x² -L „tanx - for all x €[0,1/2], then f'(x) equals 1+ ex * If f(x) = sec2x A 1+ etanx sec³x B 1+…

A: Given an integral. We need to find f'(x).

Q: At what value of x does the local max of f(x) occur? X = ƒ(x) = √² 1²-2 - 25 1 + cos² (t) dt

A:

Q: 5. Find the exact absolute maximum and absolute minimum values for 2 f(x) = cos(x) + sin´(x) on the…

A: We have to be find

Q: = sin? (esin" t) + cos-1(2t3 (x) = tanh-1 x + In V1– x2 |

A:

Q: C What is f" (x) of f(x) = x Arc sin(x) + √1 − x²? Arc sin(x) 2 √1-2² √1-7² ◄ Previous + Arc sin(x)

A:

Q: 33 2Vx- f (x) (1–3t) (t³-8) T Sin sin 2x + Ve2x + 2x – In e, x + 1 - 1-x g(t) = t # 2 2-t

A: Given:

Q: 38. f(x) = 3(sin-1 x)² %3D 40. f(x) = tan1(Inx) %3D

A:

Q: Find (f-1)(0) if (i) f(x) = 1+ sin (sin t) dt. (ii) f(x) = cos(cos t) dt. %3D (Don't try to evaluate…

A:

Q: y for the function f(x)= cos [x*sin (x²+1)] =, CoS 1/2 %3D ..…

A: The given function is fx=cos3x3sin12x2+1. Obtain the derivative as follows.

Q: sin TZ Let f (z) = Find the (z – 10)² residue of f (2)at z = 10. -

A:

Q: sin(1) Suppose F(x) = dt. Use the Fundamental of Theorem of Calculus to calculate dx (F(x). 9+1 (F<)…

A: To solve the following problem

Q: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) >= 0 for x element…

A: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) &gt;= 0 for x element…

Q: 5. Given F(x) tan(t) dt, evaluate F(0) and F'(0). 1+sin(2x) 1+ et-1

A:

Q: ez - x - 1 lim 1-0 -1+cos r COS T

A:

Q: Find the absolute extrema of the function on the closed interval.                         g(x) = 2x…

A:

Q: The domain of the function f(x)=sinh-1(Inx)

A: To find the domain of the function