[-7, 1] The average value of cos (2z)e1-sin(2z) on is

Q: Calculate cos(x) cos(y) + sin(r) sin(y) if x - y = 1. 동 0-호 ㅇ를

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Q: Part A (i) Let f(x) = ln(3ª + 8"). Find f'(x). %3D (ii) Find 2" cos(r)` cos(2") d da

A: Derivative of function

Q: The function y sin a is also which of the following functions?

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

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Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

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Q: Four equations are provided below. Which equation follows from the Power Rule? I. (P)' = pr P 1…

A: Answer is option (a)  Because only equation 3rd follows the power rule .

Q: Prove 3sin x-45 in ³x = Sin (3x)

A: To prove that,3 sinx-4 sin3x=sin3x

Q: Prove that x2 cos x dx = T(2 – n) (+ sin æ)?

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Q: f(x) = -2sin(x) Amplitude: f(x) = -3cos(x) Amplitude: f(x) = 6sin(x) f(x) = 10cos(x) %3D Amplitude:…

A: If f(x) = Asin(mt + n) or f(x) = Acos(mt + n) then amplitude = |A|

Q: A parallelogram is formed by the vectors [1, 2] and [3, -4]. Find the area of the parallelogram. O…

A: Given query is to find the area of parallelogram.

Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: a dx = 1+ sin(ax) Select one: a. tan(ax) – sec(az) + C b. ax + In | csc(az) – cot(az)| + C c. In |1+…

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Q: Determine if the setsin² {sin²x, 1-cos(2x)} is linearly dependent or linearly independent on I =…

A: Let B={sin2x,1-cos(2x)}.

Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: The derivative with respect to x of 2 cos (x² + 2) is A. 2 sin (x²+2) cos (x² + 2) -2 sin (x² + 2)…

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Q: Show that if L{f(t)} = F(s) then L{etf(t)} = F(s - k) where k is a constant. Hence find: (a) Leat…

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Q: 3 sin(0) = 8. find cot(0)

A: We will use trigonometric identity Sin2(x)+cos2(x)=1.

Q: Using the substitution t tan can be written as of dx sin(x) - 60 cos(x) of dt +30-30 2 de 30²2²…

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

Q: Let f(x) = sin(rx). Suppose that h and k are two functions such that H (x) = cos(xx), k'(x) = f(x+…

A: Given that fx = sinπx . Also given that h and k are two functions such that h'x = cosπx , k'x = fx+1…

Q: P/4 4-p dx = 4+p Prove that: x sin x+cos x

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Q: f (t) =-e" sin (21 +7)

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Q: Find the derivative of the following. a) y = cos (4x³ + x²-2) b) Y=xsin ''(x) + √√1-x²

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Q: : (a) Evaluate S cosx sinx V1 – sin+x_dx. (b) Evaluate S V1 – x² dx.

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Q: [s sin x cos x esin²x+dx = A B C D - sin x cos x esin²x+ esin²+ + C 1/2 (sin ²x + 7) + C e -…

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Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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