9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact. Ans: k=-4

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A: To Find : laplace transform of f(t)=e-tsinh(4t)

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Q: QUESTION 94. dz -22 TRIGONOMETRIC SUBTITUTION a? – u? sub. to u = a sin 0 a² + u? sub. to u = a tan…

A: Solve the following

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A: Follow the procedure given below.

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A: Here we have to find the value of b-a.

Q: The number of bacteria in a culture is given by the function n(t) = 1000e045€ where t is measured in…

A: Given problem:- The number of bacteria in a culture is given by the function   n(t) = 1000e0.45t…

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A: Now,                logb1728b=logb1728+logbb=3logb12+logbbUse logbb=1.=3logb12+1

Q: e* +cosx+sin.x– 2 3. lim xsin' x

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

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A: Explanation of the answer is as follows

Q: Q "- The value of e-(in+1)n is а) (-1)" e-я-1 b) (-1)"e" c) (-1)" e-*+1 d) (-1)" e- Q2 The period of…

A: e-ix = cosx -i sin x If y=A sinBx then period -2πB.

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Q: 4. 7 (t) = (4t, –2t, /5 t) = (4t, -21, v5 ') %3D

A: This is a problem related to vector differentiation. Based on the general formula we can calculate…

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A: Given

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A: Answer to the subparts are given ,

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A: We can solve this as follows:

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A: Given query is to find the value of the integral.

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Q: (7x-6x+8) dx |(7x - 6x + 8) dx =| /Simplifu vour anci Mor /Cimpli6 5. 5.

A: We can solve this as follows:

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A: Sequence

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A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 2. Use synthetic division to divide the first polynomial by the second. а. х? +x-33B х-1 b. 4x -Зx2…

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Q: dy 6. If y is a differentiable function of x and r + 2y3 x² = 8y?, then find dr

A: This question is based on diffrentiation chain rule.

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Q: Evaluate the following limits. If needed, enter oo for oo and -oo for 00. /3+5x2 (a) lim 3+11a V3 +…

A: LetL=limx→∞ 3+5x23+11xDivide x on N and DL=limx→∞ 3x2+53x+11L=limx→∞ 3x2+5limx→∞…

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Q: d²u A particular solution of the differential equation du - 2u=3e2t – 18e-tis dt? dt Select the…

A: Particular solution

Q: .3 29. dr 18 31. 1/2 sin (x/2 + 1) d

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Q: Let F(x) = f(x*) and G(x) = (f(x))* . You also know that a' = 11, f(a) = 2, f'(a) = 2, f'(a*) = 11…

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Q: Step 4 tan-(8x), then converting back to an expression in x we get u2 + C = 16

A: