Problem 5, Verify the following: 1. fr cos(x)dx = x sin(x) + cos(x)+c 2. ſ csc(x) cot(x)dx = – csc(x) + c 3. S = arcsec(x) + c 1 x/x²–1

Q: S .2 4. sin x cosx dx

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Q: 4. Se2x sin(3x) dx

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Q: Problem 1 Solve (x + ex sin y) dx - (y + e* cos y) dy = 0

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Q: sin x cos x y = Vx³-4

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Q: Question 4 Find the solution of the D.E. below: x cos? ydx+ tan ydy = 0 A y2+ (tanx) 2=c B x2+…

A: We will use separation of variables technique to solve the problem.

Q: Problem 7. Let Q(x) =1 – x² /6. Use the Error Bound for f(x) = sin x to show sin x Q(x) < 5! Q(x) dx…

A: The error bound of sin x is sin(x)=∑n=1∞(−1)nx2n+1(2n+1)!=x−x33!+x55!−x77!cosζ.   Then,…

Q: Problem 10. Evaluate e' sin 2t dr, correct to 4 decimal places Comparing fe' sin 2r dt with fea…

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Q: In problems 1 and 2, list both the order of the DE and state whether the DE is linear of nonlinear.…

A: Sol:- (1) tan2xy''+x2ey=2 Order = 2 (Since equation contains y'') Nonlinear

Q: Problem 12 Evaluate the indefinite integral.  ∫sin(6x)sin(7x)dx=_________________ +C

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Q: Problem 5. Prove that -dx 1+x (0 <a < 1). sin an

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Q: Question 4 Use Newton method to find a solution accurate to within 10 for the given problem: 2x cos…

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Q: Problem 1: TT/2 cos x sin(sin x) dx

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Q: 11. sin(4x) dx e 0.

A: Given: To evaluate:   The given integral.

Q: Problem 2. Solve the following trigonometric integrals. (a) f sin³ x cos³ xdx WORKSHEET 3, CALCULUS…

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Q: Problem 16. (a) Calculate the following antiderivatives: //=/ dx = (b) / -55 (c) / 2e" dx = [ -5 sin…

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Q: Problem 10. Evaluate e' sin 2t dr, correct to 4 decimal places

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Q: In problems 19-22, find L[(t)] by first using an appropriate trigonometric identity. 19. f(t) = sin…

A: Topic = Laplace transform As per guidelines , At a time only one question can be answered. please…

Q: Problem #6: Find the equation of the line tangent to f(x)= cos² x- sin? 1 at x = -. - 5x 6.

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Q: Question 14 d (tanh -'(cosx)) dx A cschx B) -csCx C) -secx D cothx

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Q: set E: Problem #6 Find the equation oF the line tangent to at x = 5r FCx) = cos?x -sin? ) %3D

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Q: Problem 4. Find the following integrals T/4 sin x (a) S Cos2 dx. Use substitution to solve it. cos?…

A: Topic = Integration As per guidelines , At a time only one question can be answered out of different…

Q: Question 2: Find the solution of the given DE (2xy cos(x?) – 2xy + 1)dx – (sin (x²) – x²)dy = 0

A: The given question is taken from the calculus in which we have to find the solution of the given…

Q: 50. S sin*2x cos“2xdx

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Q: Problem 19. Evaluate the definite integral: sin3 2x dx.

A: The integral is ∫0π/4 sin3 2x dx By using the double angle formula,…

Q: Problem 7.4. A particle moves along the x-axis such that the velocity is given by v(t) = 3t + cos(t)…

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Q: Problem 3. Prove that 2 (b) L(r} : a (a) L{sin at} : %3D s2 +a? (c) L{cosh at} : 52 – a²° -

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

Q: QUESTION 18 Compute the following. |-8sin (x) +18csc (2x)cot(2x) dx

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Q: Problem 7 Evalaute the indefinite integral.  ∫tan^5(x)sec^5(x)dx=___________________ +C

A: Consider the given integral.

Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: Problem 3.9 Find the derivative d99 (sin x) dx 99

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Q: QUESTION 6 Use differential to approximate the value of cos(48°). Give your answer correct to four…

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Q: Question 6 S sin(x) dx = a) sin ()x + C O b) - cos(x) + C O9 - cos(x)x+ C Od) x+ C

A: Given query is to find the integral of sin(π).

Q: Problem 6 The power-reduction formulas will be useful for solving which of the following trig…

A: We have to identify the integral  which can be solved using power reduction  formulas.

Q: Question 7 Find dy/dx. y = x$ sec (–) (A x3 sin 5x cos x + x² sin² 5x () B -x3 sec + 5x4 tan sec (c)…

A: here problem of differentiation we use d(u*v)/dx rule d(u*v)/dx = u*dv/dx + v*du/dx so answer is…

Q: Use the reduction formulas from problem #2, to integrate the following: a) | cos* (3x) dx

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Q: Problem 1 a) Find [(sinx + 1) ] and (sin² x +2 sinx). Compare your answers. dx dx b) What is [(2…

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Q: Problem 1: Calculate the following derivatives: (a) - (In(sin(3x))) dx (b) e+3, dx \e6x d d (c) 느…

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Q: Question 27 1 Point Evaluate: dx 9-x2 (A) 9-x2 +C B) +C sin C) sin +C (D (9-x2) /9-x2 +C

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Q: QUESTION 4 SIn(x +2) dx = O A (x +2) In(x+2)- 20x +C O B. x In(x + 2) 20 " -x+ C 20 OC (x +2) In(x…

A: Integrated by part

Q: Problem 11.8. Find the arc-length of the graphs of the following func- tions at the stated interval:…

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Q: Question 5 Solve the following initial value problems. dy (a) = 6 – 2 cos(3x) and y(0) = 10. d.x dy…

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Q: QUESTION 3 Determine the value of a that satisfy the following equation; sinhx = In(3 – a²) – In(x +…

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Q: Problem 9. Find fe" cosbx dx When integrating a product of an exponential and a sine or cosine…

A: A detailed solution is given below.

Q: Problem 1 Find the derivative for the following. (a) g(x) = Sï 7 dt (b) g(x) = Sing V1+t²dt (c) f(x)…

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Q: Problem 1. What is the distance travelled by a point during the time t, if it moves in X- Y plane…

A: Given that x=asinωt and y=a(1-cosωt) are relative to each other. We need to find the distance…

Q: QUESTION 3 a) Evaluate |x2 In | x+1| dx by using integration by parts. b) Use the trigonometric…

A: We apply integration by parts and evaluate the given integration. For part (a) follow 2nd and 3rd…

Q: Problem 2. (a) Simplify the expression cos(arctan x), x > 0.

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Q: Problem 5. Find the derivative of each of the following: d {cos(2z + 3i)}², 1) dz d {(2)[tan"'(In…

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Q: Question 2: Find the solution of the given DE (2xy cos(x?) – 2xy + 1)dx – (sin (x?) – x?)dy = 0

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Q: Problem 3.7 Find the limits (a) limz→0 sin 5x 3x (b) lime→0 cos 0–1 202 (c) limg→0 sin 3x sin 5x x²

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