Question 18. Consider the function g(x) = sin² x, in the interval [0, ¤]. Use the Trapezium Rule, dividing the interval [0, 7T] into strips of equal width d = t/2, to fine estimate for the definite integral 8(x)dx.

Q: Question 3 Evaluate the following integrals using either integration by substitution or integration…

A: we have given integral  ∫e-xsin4xdx

Q: Question 5 Evaluate the multiple integral | cos(x - y) dx dy

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Q: Question 19 Let F(x) -1. √1+t¹ dt for x in (-∞0, ∞o). Find F'(- 5 sin z O F'(x) = -√1 + cos²x O…

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Q: 1 a) I = S: dx x V4-x2 1 b) I= Sarž dx x2 V1+x2

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Q: 1. Jo cos x sinh x dx

A: Explanation and solution is given below....

Q: Question 19 Find the approximate area under the curve of f (x) =cos 5) from x = 0 to x = Tt, using 4…

A: Given- f(x)=cosx2 To find area under the given curve from x=0 to x=π, using 4 trapezoids. Here ,…

Q: If we use the fixed-point iteration to find an approximation to the fixed point that is accurate to…

A: Given that gx=π+0.5sinx and interval is x∈0,π Differentiate gx=π+0.5sinx with respect to x…

Q: (a) Find dy/dx for 3 tan x – In x x2 (b) Find f"(x) for the following function: e" In(x**) f(x) = x…

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Q: Question 1 π 2x Evaluate the integral cos(xy)dydx 4

A: ∫45∫0π2xcosxydydx

Q: Consider the family of functions h(t) = cos(3.0t) + 1.5 cos(3.6t) + 2.0 cos(vt) for various values…

A: The solution is given in the next steps below:

Q: So, 0, -T < x < 0 f (x) = sin x, 0 < x < T

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Q: A periodic function of period is defined by E sin ot, 0st< f(t) = 0, where E and o are positive…

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Q: x² – 1 Consider solving dx using a suitable trigonometric substitution. After performing…

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Q: Suppose f and f' are differentiable functions of r. Given f' () = 0, f" () -1, and g(x) = log…

A: Differentiate two times at given value

Q: * 3x ], the x-coordinates of the points on the graph of the function f(x) = 1 + cos x where the…

A: For horizontal  tangent dy/dx=0

Q: 1 16r 10. Evaluate the definite integral | dr V16-r² 11. Evaluate the definite integral 4 + sin 2x)'…

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Q: Consider a function f(x) where f" (x) = 2ª (ln 2)² + sin(-. -). 2 a) Find / f"(x) dæ. b) Assume that…

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Q: QUESTION 1 (a) Given y=cosh (x-3). Based on the given function show that d'y d'y 4 sinh (2x) ) dx''…

A: Given that, y=cosh2x-3 To prove, 14sinh2xd3ydx3+d2ydx2-tanhx-3dydx=2y+1  But i think it should be,…

Q: QUESTION 3: Calculate and interpret the condition numbers of the following functions. a) f(x) = lx-1…

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Q: Question 2 Find the linear approximation of the function at the given point. f(x, v) = 3 sinx - 7…

A: F(x,y)=3 sin x - 7 cos y at ( 0 , π/2)

Q: An Alternating current "i" at any time t is given by i = sin 3t.Find the RMS Value of the current…

A: This question is related to integration.

Q: Question 4 a. Solve the following definite integrals. xp (* + x^€) ,'J (V&+1)* dx

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Q: Suppose f and f' are differentiable functions of r. Given f' () = 0, s" (÷) = -1, and g(r) = log…

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Q: Question 2 Estimate the integral sin? x ) dx by the trapezoidal rule using n = 5. а) О0.7000 b)…

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Q: QUESTION 3 Solve the IVP d3 at3 (t) + 9 x(t) =27 sin(3t) + 18 e-3t dt dt x(0) =8 x'(0) = 9 x"(0) =…

A: Since you have asked more than one question, we will solve first one for you. If you want any other…

Q: H.W 3 1. plot the below function in the range 0 to 3r in steps of /20. sin(x) y(x)= { sin(x) 20…

A: Kindly ask only one question.

Q: Question 4. Show that the average value of f(x) ei. = e- + cos x on the interval [-7/2,0] is

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Q: Question 9 Let y = tan e find the differential dy of the function. O dy = e (r – 1) sec e- da O dy =…

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Q: 1. Find the general indefinite integral. 5e + 3 sin x dx (b) ["be²

A: We have to solve this given integral . For this first we solve the general indefinite integral &amp;…

Q: 2 Consider solving dx using a suitable trigonometric substitution. After performing substitution…

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Q: QUESTION 2 Use the definition of differentiability to show that the function f(x, y) = cos(x² + xy)…

A: Given function: fx,y=cosx2+xy Function fx,y is differentiable at x0,y0 if: ∂f∂xx0,y0 and ∂f∂yx0,y0…

Q: - Find the extrema of the function f(x)=5 sin(2.x) – 2x? – 4x - Using Newton's method initial quess…

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Q: Question 5 Estimate the integral sin* () dx by Simpson's rule using n = 4. a) О0.12082 b) 0.06041 O…

A: Apply Simpsons rule…

Q: Question 2 Differentiate the following functions (i) If y= e-t sin 4t, prove that +6+2y = 0. (ii)…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU AS PER…

Q: Question 8 Let y = tan find the differential dy of the function. O dy = e* (x² – 1) sec² \ e*"-1 dæ…

A: As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And ddxtanx=sec2xddxex=ex…

Q: 5. What is the maximum value of the transformed sine function g(x) = -2 sin[3(x + )] – 6? А. —4 В.…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Question 13 Evaluate the integral J sinh? (2x)cosh(2x) dc sinh“(2x) +C A sinh(2x) +C B 9 costf(2x)…

A: Use the derivative identity, ddx(sinh(ax))=acosh(ax) And the power rule of integration is:…

Q: QUESTION 1 Estimate the integrals of I, both analytically and numerically by using Multiple…

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Q: Consider the function f(x) = cos x -3x+1. Since f (0)f () <0, f(x) has a root in [o]. If we use…

A: Given that                     f(x)=cos x-3x+1 Newton-Raphson iteration scheme is…

Q: 2. If you know (1 – a.0 s a s 1 * f(x) cos ax dx = 0 ,a>1 Find the value f(x)!

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Q: QUESTION 4 For the given function f(x) = cosx, let xo 0.2, X1 0.4, and x2 = 0.7. Find the Error…

A: Given - For the given function fx = cosx, let x0 = 0.2, x1 = 0.4, and x2 = 0.7 To find - Find the…

Q: Question 1 (i) Determine the following integrals (a) |cos? xsin xdx 1 -dx (b) J -5x+6 x² – (c)…

A: We have to find the integrals.

Q: Question 14. Obtain the following integral I where: [z sin(3=)dz I= as a function of æ, to within an…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Question 6 a. Solve the following integrals: i. Scos x) sin (-) dx il. SeVI+e*dx

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Q: Question 26 What is the maximum value of f(t) = sin t + cos t in the interval 0 <t < /2 O 2/2 O 2 O…

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Q: 9. If f is an always positive, differentiable function and y = In (f (sin x)), what is- dy when x =…

A: Explanation of the answer is as follows

Q: 1. Determine the relative extrema of the function y = 2 cos x + sin 2x on the interval (0, 2Tt). %3D

A: To find the extrema of the function

Q: (c) 1. f(t) dt = In(x) cos(x)+ sin(3) L e-" f(t) dt, find f(x). You may find FTC 1 useful. sin(3)…

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Q: Question 6 Given: f (x, y, z) = cos(xyz) + ln x5 - sinh y² + 3z Find: af(x, y, z) дz at P(-1, 3, 0)…

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