Evaluate L{t² cos t}

Q: d -1 ) Prove that cos 1(x) : dx V1-1

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Q: A. cos (T – n1) n=1

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Use the Fundamental Theorem of Calculus to find (2 + cos x) dx.

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Q: (b) Let f(x) = sin (cos-1 (sin(cos-vx))).B f'(1) = using chain rule, show that %3D

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Q: -t 2 lim 8 cos t ||

A: Given  The limit is limt→π2t2-π2t8cos t

Q: (a) f(x) =cos (7æ) cos (Tx) 3

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Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is f'(pi/4)=4

A: sol:-    Given f(x) = (x+ln(cosx)  differentiating ω. r.t   x, we get    f1(x) = c+1cosx(-sin x)…

Q: 2. Find the domain of the function. cos x b. f(x) = 1 - sin x

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Q: Compute S x? cos(x³ + 3) dx

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Q: Prove the identity cos(x+y)cos y +sin(x+ y)siny =cos x

A: We have to prove the identity                              cosx+ycosy+sinx+ysiny=cosx

Q: ) prove thaE cos ( x) dx =- T e x" + x2 +l 213

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Q: prove the identity  sin^4(t) - cos^4(t) = 2sin^2(t) - 1

A: We know that ,  sin 2 ( t ) + cos 2 ( t ) = 1  cos2 ( t ) = 1 - sin 2 ( t )

Q: n+1 Evaluate lim cos“(x²)dx n→∞ (and show all work)

A: The required results are as follows: cos2 x=12+12·cos(2x) and cos 2x=1-(2x)22!+(2x)44!-(2x)66!+...…

Q: If tan then 1– 2 1+ z2 COS X 8 |N

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Q: Evaluate | e'(sin(1) + e*)°dt using an appropriate substitution.

A: Given : ∫etsin1+et9dt

Q: sin (21 + 1) dt J cos² (21 + 1)

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

Q: Locate and identify the absolute extreme values of cos (ln x) on [1/ 2, 2].

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Q: y = x cos(In x)+x² In x²

A: d dx(cosx) = -sinxddx(lnx) = 1xddxx2 = 2x   Product rule u.v = u'.v + v'.u

Q: Calculate fsin³ a cos° a dx.

A: Let cosx = t Differentiate on both side   - sinx. dx = dt    sinx. dx =  - dt

Q: Compute the following: sin² (x) dx

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Q: 3. Prove that the identity is true. sin*t - costt tan-t– 1 cos't

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 8. Show that cos a – cos y| < |x – y| for all æ and y.

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Q: Find 1+sin -cos I COS In | sin - z+cos In In 1+tan +C +C +C +C

A: We can evaluate the given integral by using the substitution u = tan (x/2).

Q: Find wronksian is w ( cos x,sin x)

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Q: O cos Z 12 15

A: Right angle triangle

Q: tan (t) dt. Evaluate cos® (t)

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Q: Assume sin(t) = -12 where π < t <3. Compute the following: csc (-t) = cos(t + 2) = tan(t) =

A: We have given  Sint = -1/12 , where π&lt;t&lt;3π/2  Compute  1) cosec(-t)  2) cos(t+π/2)  3)…

Q: Calculate L4 for f(x) = 84 cos ()

A: Given,           f(x)=84cosx2  over 2π4, 2π2

Q: COS x Compute r4 + x2 + 1 8.

A: Given integral is I=∫-∞∞cosxx4+x2+1dx Now, it is known that cosx≤1 for all x∈ℝ. Therefore,…

Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: Find the value of ∫tsin(t)cos(t)

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Q: 4 + cos t -dt 1 – sin t

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Q: Find y' if y = arcsin cos x O -2 O 2 O 1 O-1

A: Solution

Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

Q: Determine f,(x); f(x) = cos(2x³ +n²)

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Q: b) verify the functions sin(3x) and cos(3x) are linear dependent or Linear independent.

A: Hence linear independent

Q: 1. Evaluate the integral 7/2 cos xesinx *dx

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Q: Prove the identity. TC cos = tanx %3D cos (T+x)

A: To Prove:

Q: e* (1 + sin x de. nx] Evaluate 1 + cos x

A: I am attaching image so that you understand each and every step.

Q: Verify the identity: (1 - cos t)/(1 + cos t) = (csc t - cot t)2

A: Given: 1-cost1+cost=csc t-cot t2

Q: إعادة تعيين Q5. Let a and b be distinct nonnegative integer. Prove that sinax cos bx dx = 0 إلغاء

A: We will find the value of integration.  We know the formula of  2sinA cos B = sin(A+B) + sin(A-B).

Q: Fand ar a of functrons COSX n

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Q: Prove that 55 sin x² dx - 5 cos x² dx = 1/2 √

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Q: Prove that cos (÷+t) = - sin t

A: We have to prove that cos(π\2 + t) = -sint

Q: iv) Evaluate fsin' x cos² x dx .

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Q: Prove that : n/2 1 dx (a'sin'x + b’cos'x 4a°b³

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Q: Express T(x)sin x-root(3)cos x into the form of T(x)=Asin(x+theta) , where A>0

A: Sin(A+B)=sinAcosB + cosAsinB

Q: find Fourier sertes [0, 2w] an O f = X COS X

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is  f '(π/4) = 9?

A: Consider the given function, fx=cx+lncosx first differentiate the function using chain rule as…

Q: Prove the identities: (x sin 0 – y cos 0)² + (x cos 0 + y sin 0)² = x² + y²

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