EXERCISE: 1. Approximate the following integrals using the Trapezoidal rule and Find a bound for the error using the error formula, and compare this to the actual error. dx a- Jas b-

Q: Cyrus deposit $744.88 Each quarter into an annuity account for his child college fund. He wishes to…

A: Given that Cyrus deposited $744.88 each quarter into an annuity account. The future value he wish to…

Q: Tnd th gredient y te tengut y= 3x at te pont (3,-1)

A: See the detailed solution below.

Q: we draw a tangent line on y=/25 –x² at x = -3. 14 - find the slope of this tangent line. O A) 2/3…

A: To find- slope of the tangent line.

Q: Use the trapezoid rule withn=4 to estimate dx . Answer must be in fraction.

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Q: PIND F'): b. FG)- 4- ax*)

A: Given: f(x) = 4-3x25 To find: f'(x)

Q: dy for the function y = dx 7) Using the first principles definition, determine 2x

A: topic - derivative of a function

Q: Q4) find at t= from the following functions, x= cost . y= 1+sint

A: Given that  x=cost  y=1+sint  To find the d^2y/dx^2 at t=π/2

Q: Evaluate: x2dz using trapezoidal method with n = 10. Round off to 6 decimal places.

A: To evaluate using the trapezoidal rule with n=10.

Q: Q1: Use the data below to find the focal length of convex lens by plot between 1/u & 1/v: 1/ u…

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Q: Find the sope to the tangent Iine of the equation ,-y +ear (0,3) Hirt perform impl cit…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: y = -V16 – x², — х2, -4 < x < 0.

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Q: Find the tangent X = 3t² + t Y = 4+³ 3 line t = 1 to the curve

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Q: s(t)=-t2+6t 1)Find displacement after 5 seconds 2) Find the distance traveled after 5 seconds

A: Given 1) Displacement after 5 seconds is

Q: 2 -e dy=x(xdy-ydx).

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Q: Show that: (e) (VF) = 1 dx

A: Derivative of a function xn: ddxxn=nxn-1                               (1) Given function is: f(x)=x…

Q: For the function y = x² + 2x, the value of dy when *=3 and dx=0.1 js -0.15 A) 0.15 B) C) - 0.8 0.8…

A: We will find out the required value.

Q: Solve by using Homogenous differential equation method: 3- dy Зу dx X +tan() X

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Q: Q4.a) Construct the cubic splines for f(x)=xlnx with x-8.3, x-8.6. Approximate f(8.4) and f'(8.4),…

A: To construct cubic splines for the function f(x) = x * ln(x) using the given data points x = 8.3 and…

Q: Q3 Determine the area of a surface when the curve y==x² 3 1 x², 1<x<3, is revolved about 2 the…

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Q: Approximate / 1+r² dr using four rectangles and the left endpoint method (L4).

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Q: Use n = 6 subdivisions to approximate the value of Vx +2 dx by the trapezoidal rule.

A: The given integral is ∫06x+2dx and the value of n is 6. Using the trapezoidal rule, approximate the…

Q: Use a tangent plane at the point (4, -—4) to approximate the value of the following function at the…

A: Tangent plane to the surface

Q: dx Evaluate using trig substitution: a x'V4-x? upo an

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Q: Approximate 4 1 dx 1+ x Using the Trapezoidal rule and Simpson's rule with h=1. Find an error in…

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Q: dy Find for the given functions. dx3 a) y = /2x + 3 b) y = 2.x – 1

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Q: dy (1 + æ)* Find for y dx Ans=

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Q: Q2:Fid for : y = dy ncothx + sechx* dx

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Q: Find a 3 x 3 matrix A such that A = 97 for all in R³. A =

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Q: 2 In? x dx

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