Evaluate the following integrals using Trigonometric Substitution: x-1- 16x dx x 2. dx 9 dx 25t2 - 1 dt 5. X /4 + x dx

Q: Let F(x) = (f(x))² + (f'(x))², F(0) = 6, where f(x) is a thrice differentiable function such that…

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Q: Given the points A(-2, 3, 1), B(0, 0, 2), and C(-1, 5, -2) Determine ZBAC, the angle between AB and…

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Q: (D³ - 7D + 6)y = 0 %3D

A: Differential equation

Q: Write down the gradient of the straight line represented by the equation y = −0.05t + 47. What does…

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Q: For the curve defined by *(t) = 2 cos(t)i +2 sin(t)j + 3tk evaluate F (2)||du S = to find the arc…

A: Given that the curve  r→t = 2 costi→ + 2 sintj→ +3tk→  = f(t)i→+g(t)j→+ h(t)k→        we  have to…

Q: Find, the genetal Solution o the differehtial equation (2x+Y-3) dy= +2Y-3)dXf %3D

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Q: y 5| 3 2 -4 -2 -1F 4. 2.

A: We find the point where limit does not exist

Q: 2. All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: We have to find changing the surface area

Q: dx 5x2 + 16

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Q: Find the arc length parameter along the given curve from the point where t=0 by evaluating the…

A: We have to find the arc length.

Q: dx 8. Evaluate the integral / zlnrV(In x)² – 8 x In a V(In a)2 – 8 |

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Q: 0:32:4 Consider the solid obtained by rotating the region bounded by the given curves about the…

A: Given problem:- Consider the solid obtained by rotating the region bounded by the given curves about…

Q: 18 C. Solve as indicated. 4. A car costs Php 800,000. Find its value after 4 years if it depreciates…

A: car cost Php 800000 value after 4 year = ? per year depreciate is 20% 800000*20/100 = 160000…

Q: The radius of a circle is found to be 7 cm in length with a possible error of no more than 0.04 cm.…

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Q: Find the minimum and maximum values of the function y = 8Vx? +1 – 5x on the interval [0, 3] by…

A: To find the minimum and maximum values of the function y=8x2+1-5x on the interval 0, 3 by comparing…

Q: SIn(5 + VT)dr Algebraic Substitution

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Q: ) Eliminate the arbitrary umstants of y= C, + C2 e ** + C3 e 3x

A: The given equation is y=c1+c2e2x+c3e-3x. We have to eliminate arbitrary constants c1, c2, c3. Since…

Q: Find the differential dy: y = In (sec2 (3* )). -2a+5 O tan (3-2+* ) dæ -2r+5 dy = (x – 1)…

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Q: Evaluate the indefinite integral. for, sin( + C

A: Product Rule of integration : ∫u.v dx= u∫v dx - ∫dudx∫v dxdx .

Q: A. Find the area of the plane region bounded by the given curves 1. y = x, y = 2x, and x +y = 6…

A: Note: As per our guidelines we are restricted to solve only one problem. Please upload separately…

Q: Given r = 1 – 3 sin 0, find the following. Find the area of the inner loop of the given polar curve…

A: Concept: Area in polar coordinates: various regions enclosed by such curves can be calculated using…

Q: x3-1 dx J2+2x+5

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Q: 6s – 4 s2 – 4s + 20

A: 6s-4s2-4s+20=6s-4s2-4s+4+16=6s-12+8s-22+16=6(s-2)+8s-22+16=6·(s-2)s-22+(4)2+8·1s-22+16

Q: Let p(x) be a polynomial of degree 3. Its derivatives, around the point æ = -5, are as follows:…

A: solution:-let p(x) be a polynomial of degree 3p(x)=ax3+bx2+cx+dwhere a,b,c & d are parametersat…

Q: (D² – 2D – 3)y = 64xe³*

A: The given differential equation is:D2-2D-3y=64xe3xWe will solve this by method of undetermined…

Q: cos 0 tan 0 + sin 0 Express as a single trigonometric function of 0. cos 0

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Q: 4. A car costs Php 800,000. Find its value after 4 years if it depreciates 20% of its cost per year.

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Q: - If f(r) = e² is a solution of xy" – (r + 1)/ + y = 0. Then, the general so (A) y = c1e² + c2e=z…

A: Answer is in next step     option  E is correct.

Q: Triangle BAC is a 30°°-60°°-90°° right triangle. 600 30° A C If BC = 15, what is the measure of AC?…

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Q: 3s 14 82-4s +8 - 3e cos 2t + 4e2" sin2t 3et cos 2t –4e2" sin2t - Option 1 O Option 2 4e2t cos 2t +…

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Q: e2t (t3 + 5t – 2) - 6+ 5(s – 2)? – 2(s – 2)³ (s – 2)* 6 2 - | (s + 2)* (s – 2)? 8 – 2 Option 2…

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Q: (a) Solve the equation on the given interval, expressing the solution for x in terms of inverse…

A: Let's find.

Q: A man of height 1.7 meters walks away from a 5-meter lamppost at a speed of 1.5 m/s. Find the rate…

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Q: 4s + 12 82 + 88 + 10 4e-4t 4te-4t 4et + 4tet - Option 3 Option 2 4et 4tet - None of the choices…

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Q: Two similar-looking series are given. Test each one for convergence or divergence. 3" ( a) Σ 3" (6)…

A: To test for convergence and divergence for the given series.

Q: A particle is moving with acceleration given by the function a(t) = sin t - 3t. Find the position…

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Q: 4 -2 3 1 3 2 15) - 2 1 Ans. -3, 2 ; 5, 0 1 2 2

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Q: 3 Use the linear approximation to estimate Af = f(3.1) – f(3) for f(x) = I+x (Use decimal notation.…

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Q: dx x3+27 8. Evaluate

A: We have to find the integral

Q: 29 – 49 - dy C. 2+ 4y · Evaluate using substitution

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Q: _5. Given the fox²dx, which of the following is the integrand? A. O B. 2 C. x D. dx

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Q: 3. A right circular cone has a base radius of 6 feet and slant height of 10 feet. If the approximate…

A: Solved below.

Q: NONHOMOGENEOUS EQUATIONS: UNDETERMINED COEFFICIENTS  2. (D^2+D-2)y=2x-40cos2x Please answer this…

A: Here, the given DE is: (D2+D-2)y=2x-40cos 2x Now, to find the yh. The auxiliary equation of the…

Q: Problem #7: (a) Solve the initial value problem (x - 1)y' - y = 16(x - 1), (2) = 0 (b) Write the…

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Q: 2x e dx 4e2a –8e* +5 -

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Q: Use the Root Test to determine whether the series convergent or divergent. n2 + 1 9n2 + 8 n- 1…

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Q: oint) Use the graph of f(x) shown below to find the following integrals.

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Q: The average amount of time that a customer waits in line for service is given by W(x, y) = y < x…

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Q: Determine dydx of function g 1 g(x, y) = cos (Tx ) + log3 (x – y)

A: We will use simple differentiation rules to solve this question.

Q: 4x +3y -5z =5 -3x +3y -15z = 18 -5x -2y +5z =-9

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