-х- 2, х<-1 -1, f(x) =. -1sx< 0 at x = -1, 1, 0 sin(2tX), 0

Q: * (D'+1)y(x) = tan(x) 1-sin(x) 1+sin(x) 1+cos(x) - y,(x) = sin(x)In m(x)s03 = (x) 2- -- y,(x) =…

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Q: 1 lim h-0 2h sin(x²)dx = %3D -2h O cos(1) sin(1)

A: Using Fundamental theorem of calculus: ∫-2h0sin(x2)dx=sin(0)-sin((-2h)2)=0-sin(4h2)=-sin(4h2)

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…

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Q: f(x) 3 cos x 2 tan x - - f'(x) = f' 3 r()-

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Q: Increasing and decreasing functions Find the intervals onwhich f is increasing and decreasing.

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

Q: 2 n- tan x sec"- 9. Show that for n > 2, п-2 sec" x dx + n - sec" 1 x dx п — 1 | 4 Use this to find…

A: You need to use reduction formula to integrate the function, such that: You need to use integration…

Q: Topic: Variable Separable and Homogenouse D.E. I need particular solution for 4

A: We have to solve

Q: Ruestion 13 Evaluate the integral. x4 - 3 dx 2 16 + x o 3.253x + tan 1주 + 253 글x-16x + tan1 +C 16x +…

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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.

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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

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

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: 1. n! n=0 2. (-1)"x2n (2n)! 3. (-1)"x2n+1 2n + 1 n=0 x2n+1 4. E(-1)"- (2n + 1)! n=0 A. sin(x) B. e*…

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Q: 1) Find All solutions For y = 3.0 to the Transcendental equation: sinx-ln z = X - Y + gamma x This…

A: note : we will refer the term "gamma" at the end of the  equation as the symbolical constant : γ =…

Q: f (x) = cos(x) f(x) = tan(sin(x)) g(x) = In(2x2 + 4x + 3)

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Q: 1+sin x sin x <x<0 6 -- If f(x) = {b , x = 0 is continuous at x = 0, find the values of a and b. tan…

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Q: 3-f(x) = tanh¯1(cos(e*))

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Q: -2,2] R, then show that the function sin for x 0, f(x) = for x 0, aly continuous.

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that f (x) = x − cos x has a…

A: Consider  Where x belongs to the interval [0, 1] Since x and cos x both are continuous on [0, 1].…

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

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Q: Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that          f(x) = x - cosx…

A: As the intermediate value theorem states that if a function is continuous on a closed interval [a,b]…

Q: II. Definite Integral x²dx 1. 3 (1-x3)7 2. sin³ ydy

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Q: (-1)° x*1 (2k –1)! 2k-1 k=0 a) sin x b) cosx c) sin x- x d) cosx-1 e) e* ||

A: Given,

Q: Q4 1-F(x)=limx→0 vV(x2+3)-3}/x2 2- limy 3y+5y2-7 10y3-11y+12 sin4x 3 - lim 0 sin2x

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Q: -x² 9 d. f (x) = xe [0, 5]. e. f(x) = |x² − 4], [0,3]. sin x f. f(x) = = [-ㅠ -π, π]. x² + 1

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Q: Limit -1 to 1 integral (1-1/2 x) dx

A: Given:        ∫-111 - 12x dx   To find the value of ∫-111 - 12x dx   Formula:          ∫xn dx = xn…

Q: 1-T= 3- Z= +cos(y)tan ( √x-b cos (n) 2-sin²(n) 2-B=sin(x) sec(x)/cscf(x) 4-(w+n)²(a+) x-3

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Q: 4) f(x) = V1- x² sin-(2x + 1). %3D y 5) tan(x - v) =

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Q: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

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Q: (x² +1)Z. tan-1(sin 2x) Q2/ B/Find dy if у 3 dx (x2 +4)3 . sin-32x

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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…

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Q: SV1+ sin2(x - 2). sin (x – 2). cos (x – 2) dx

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

Q: 4) f(x)= cos x COS X %3D (5) f(x)=xsinx -1+ Cos nx

A: Since you post more than one question. As per our guideline we can solve only first question for…

Q: (1) y = In(x+ 4)- x tan (2) xy + xy x + 3y (3) Iny e' sin

A: In this question we will use basic of calculus i.e concept of differentiation. We will simply…

Q: 4. Find the absolute maximum and absolute minimum of the function f(x) = 3 sin(x) cos(x) over the…

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Q: sin(bx)+a x<0 f(x)=< | sin (2x)+2x x20 which is differentiable everywhere, then what are values of a…

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Q: 1– tan(*,) [1– sin x] lim 1+ tan(x (¥2) [z – 2x] x- - 2 1/8 1/32

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Q: sech x+csch x Q3: prove that e2x %3D csch x-sech x

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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

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Q: cos x 13. lim x-(7/2)* 1 – sin x e21 – 1 15. lim - -0 sin t 1 - sin 0 17. lim 0/2 1 + cos 20

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

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Q: 5. y = tan-¹tan x] ab 6. f(x) = x² cos-¹¹-√x²-1 7. f(x) = tan ¹(sin² (2x)) 8. y = (cot ¹(sin¹(x))³

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Q: x(x² + 1)² 1. f(x) = ln 2x3 – 1 3 sin-1(x In r

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: k. f(x)=cosh(x³)+ sinh(10x) 1. f(x)=In(x* +1)

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