Evaluate * e2x sin e" dx : -e*cos(e*) + sin (e*) + c e*cos(e*) – sin (e*) + c Option 1 Option 3 -e*cos(e*) – sin (e*) + c e*cos(e*) + sin (e*) + c Option 4 O Option 2

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Q: (5* )csch x²+1 dy if Find dx 1. (a) y = x >0. (ecosh 5x) In Vx +1 )

A: Find your answer below

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A: ∫ xdx/(1-x2)3/2 here assume that  1-x2 = u -2x = du/dx xdx = -du/2 ∫ -du/2u3/2 ∫ -u-3/2du/2 2u-1/2/2…

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A: I

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Q: sin r da 4.

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

Q: 4. If E-1X = 60 and E-1 x = 90, find each of the following: E(x - 7) a. b. Σ-7 E(xi + 2) C.

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A: Apologies for the inconvenience. Here is the complete solution:   Given series is = ∑n=1∞an where…

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Q: Evaluate the limit. (Use symbolic notation and fractions where needed.) tan(4x) lim x-0 3x

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Q: Solve the differential equation with the appropriate method. Finalize the answer equated to y. 1.…

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Q: Solve the following differential equations using the method of undetermined coefficients. y" + 4y' +…

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Q: [p'(8+3p*)®dp

A: Given: I=∫p78+3p48dp  ...1   The Power rule: ∫xndx=xn+1n+1+C

Q: B) By using (A), Find lim /-

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Q: 12) The solution of 2lnx-In(x+ 2)=In2 is a) 0 b) 1 c) {-1,4) d) 4 e) поп 13) sin( 2 csc"1(2)) = b) -…

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Q: Find the area bounded by these curves. (All choices are in sq. units) Y1 = (x – 2)? Y2 = x

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: To use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: Consider the function f (x) = -4x2 + 8x - 1. %3D Step 2 of 2: Interpret the meaning of f '(-9) = 80.…

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Q: Consider the following. u = 5i + 4j, v = 31 + 2j (a) Find the projection of u onto v. 33 3i + 2j 13…

A: u = 5i +4j v= 3i+2j   a projection of u onto v  = (u*v)v/|v|2 u*v = 15 +8 =23 |v|2 = (32+22)2 = 13…

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Q: d (cosh* 3x– sinh* 3x)= In(x + Vx² -1). -1 (b) Show that for x 2 1, coshx- - dr

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Q: Express the limit as a definite integral on the given interval. lim > x; In(2 + x;2) Ax, [2, 5] n-…

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Q: Determine whether the following equality is true or false. 2-x2 D -1 x where D = {(x,y)| xr² + y²…

A: ∫∫Df(x,y) dA = ∫x1x2∫y1y2 f(x,y) dy dx.