cosh (T- i) = %3D e cosl - i e sin 1 + e-I cos 1 + i e- sin 1 e cosl - i e sin 1 + e-T cos 1 ie-I sin 1 e cosl + i e sin 1 e cos 1 + i e T sin 1 - e cosl - i e sin 1 + e cos 1 + ie sin 1 TT 2.

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A: 4. In this question, we need to find the integral.

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Q: 6) Find all relative extrema in the function h(x)=cos on the interval [0, 2].

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A: We know that, The expression for the integration by parts: ∫udv=u·v-∫vdu   Given: I=∫exsin3xdx

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A: we need to integrate ∫0πe-tcose-t dt   we can do this integration by substitution.

Q: 6. What is the average rate of change of the function f(x) = cos x over the interval ↑ <x< 2n? A. 27…

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Q: Write S, = E(-1)i-la; where i=1 in ai = (-1)–1 sin x dx. (i–1)ñ x Show that a; > 0 and (an) is…

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Q: sin x – x dx = ? X 22n (a) E(-1)". 22n+2 (b) E(-1)". (2n).(2n)! (2n +2).(2n+2)! n=1 n=1 22n+1 22n-1…

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Q: 4. dx J x Inx VInx2 -1 A C - sec-1 (In xx) + C sec-1 - In x sec-1 (In x) + C + C In x. sec-1 O A В E…

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Q: A s = e B s = cos(2) C s = e1/2

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Q: 2n X f(p sin()cos(0) p sin ()sin(e) • p cos(o) p'sin (4) f(x, y, z) dV = dp de de Jn/2

A: SPHERICAL COORDINATES : The spherical coordinates are : x=ρsin θcosϕy=ρsin θ sinϕz=ρcosθJ=ρ2sinθ…

Q: Find y': e siny + e cosx - a. none of these e sinz+e siny e cosy-e cosa e sinx-e siny ex cosy+eycosx…

A: Find y'

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Q: dy Y=sin x dx x O x(y +cos x ) = sin x +c O x(y - sin x ) = sin x +c O x(y +cos x ) = cos x +c O x(y…

A: topic - differential equations

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Q: Find the total differential. z = x cos(y) - y cos(x) dz = (No Response)

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Q: (a) Find the MacLaurin polynomial of degree 9 for the function h(x) = ln(1 + x3). (b) Use you answer…

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Q: aw Find for w e" sin p where ax p = sin x q = z2 In y x- at (x,y,z)3글) %3D z2 e sin-1 x = Hint: dx…

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Q: 1- Find the average rate of change for y = xo = 1 x, = 2 2- Find the instantaneous rare of change…

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Q: dx 3. Evaluate: S V(x+2)(3-x) A. sin-1 (*) + 3x- C.V6 +x – x² -In |x-+v6 + x – x² |+C B. sin-1 (*)-…

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

Q: y2) = Br* -cos x. %3D A. 24x2 B. 24x + sin x+2 Given h(x) = -sec²x, determine the general…

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Q: x dx = e* + cos x e* + sin x O a. In(e* +sin x)+C O b. In(e* + cos x)+C О с. - In(e* + cos x) + C…

A: To evaluate  ∫ex + cos xex + sin x dx

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Q: e) S„ =E(-1)". sin (5 +n5) Vn+1 e) S. = n=0

A: Note:-  Sum of convergent and divergent series is divergent. cos2x=1-2sin2x⇒sin2x==121-cos2xput…

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Q: 1. S(tan -1)ʻ dp 2. sin2 B cos B dB .5 xdx 3. S (-7-8x-x* 4. Sx³ (a2 + x2) dx xdx 5. f (x²+a²)³ 6.…

A: (2)

Q: 30.f e dx = A.-e + k 31.fe*sinxdx A.-½ e (cosx + sinx) +k C. e (cosx + sinx) + k 32. In(x*) dx - %3!…

A: The formula for integrating by parts is given by;

Q: Test ODE for exactness (sin y cos y + x cos² y)dx + x dy = 0

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Q: sin x – x dx = ? %3D 22n (a) E(-1)". 22n+2 (2n + 2).(2n+ 2)! (2n).(2n)! (b) E(-1)"- n=1 n=1 22n+1…

A: ∫02sin x-xxdx

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A: Applying Leibniz's rule

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Q: A. Bernoulli 's Equation e-2x 3 1. yl =y- xy°c %3D | 2. ( 3 tan X 2 cos y) sto xdx t tan xsin ydy -…

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Q: [(1- sinx) dx cos'x sinx COSX cos?x %3D COSX %3D = |(sec2 secx tanx) dx = tanx - secx + c. ACAS a a…

A: As per the guidelines we are suppose to answer only first 3 subparts. Please repost the rest of the…

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Q: Beta Function x dx 3/3 dy (h) 1+ 142/2 that (a)

A: In the given question, the concept of the Beta function is applied. Beta Function is expressed as-…

Q: sinh (z) = %3D e -e 2- e?+ez e2+ez 21 eiz +e-iz 2.

A: We need to find the value of the function sinh(z) Four options are given. So the solution to the…

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Q: Can you please check my work for question 14? I know it it hard to follow, but I don't know if I got…

A: The given equation is,

Q: Prove the identity. sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y) sinh(x) cosh(y) + cosh(x)…

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Q: Solve the separable equation y(3+ sin(x²))dy = xcos(x?)dx subject to y(0) = -Vā where a > 0 is a…

A: Given that, y3+sinx2dy=xcosx2dx

Q: = 0,0 < x < a,0 < y < b dy dx² и(0, у) 3D 0, и(а, у) 3D 0,0 <у <b u(x, 0) = 1, u(x, b) = x, 0 < x <…

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Q: S cosh x · sinh x dx = Select one: cosh*x а. 4 cosh* x + c 4 b. sinh x С. O d. - sinh + c x

A: Explanation of the solution is given below....