ƒ (t) = (sin(t) — ¼ t³)³ - 3 9 g(y) = (2y — 5)-4 — 2² (2y – 5)-² -5 f(x) = (√x + x)¯°h(x) where h(x) is an arbitrary differentiable function.

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x A 1.

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A: topic- indefinite integral 2sinθcos(θ)=sin(2θ)sin2(θ)=1-cos(2θ)2

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Q: 3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

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Q: 1.5 Integrate 10(2x + 1) dx Answer 1

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Q: 10. Let w = f(x, y, z) = xe. If x = t², y = 1-t₁ z = 1 + 2t, use the partial dw dt derivatives and…

A: Using the chain rule and rule of partial derivative and get the required derivative.Final solution…

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A: The given equation x2+3y2=r2

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Q: 5. Integrate the function below, if the answer is expressed as (a/b)*pi + 2*In(c), find the value of…

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Q: Find all the values of x such that the given series would converge. (x-8)" 8n n=1 The series is…

A: We will use ratio test.

Q: dy dx Q5: Find for the following functions: (2) y = tan³√√cot(7x);

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Q: Integrate using the method of trigonometric substitution. Express the final answer in terms of the…

A: In this question we have to Integrate using the method of trigonometric substitution.

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

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Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y = 11e2x, y(0) = 1, y'(0) = 1 2x -7.x 7e…

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 2 (1) limx-o[: 1-cos x sin²x (2)…

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Q: The figure to the right shows the area of regions bounded by the graph of f and the x-axis. Evaluate…

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Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim-00 2n+1 2. log10 (3x…

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Q: At what rate is the angle between a clock's minute and hour hands changing at 7 o'clock in the…

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Q: Find the indefinite integral using any method. (Use C for the constant of integration.) (sin(0) +…

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Q: 2 x²log₂ (x) dx S

A: Please show complete solution. (Use integration by parts)

Q: (B): Find the tangent equation to the curve y = sin² x at point x = = 33.

A: The curve y=sin2x at point x=π3

Q: 8 If f(x) = 3 + = + x 6 x2 find f'(x). Find f'(4). Round to 3 decimal places if necessary.

A: Given that f(x)=3+8x+6x2-(i)Our Aim is to find f'(x) and f'(4).

Q: Use the remainder theorem to evaluate the polynomial for the given values of x. g(x)=6x³-7x²-36x+42…

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Q: Find f(145) (x) for f(x) = 83x¹0⁹. Simplify your answer completely. f (145) (x) =

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Q: (a) State the Fundamental Theorem of Calculus Part I √x (b) If G(x) = cos(t¹) dt, compute Gʻ(z). (c)…

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Q: Q4: (chose one only) 3-x 1- f(x) = 2 x 2 a) Find limx→2+ f(x), limx→2- f(x) andf(2). b) Dose limx-2…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: find an equation in spherical coordinates for the equation given in rectangular coordinates x^2 +…

A: We have to find spherical coordinates form

Q: Find all points where the function is discontinuous. Ox=1 O None O x = -2 Ox= -2, x = 1 →→x

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Q: Find both first partial derivatives. z=(4 xy)/(x^2+y^2) fx(x,y)= fy(x,y)=

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Q: (xx) 2. 6. 3. 7. 8. 9. 10. 11. 16. 17. 12. 18. 19. 13. 14. 15. To divide a decimal number by 1000,…

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Q: Q5: Find d for the following functions: dx (1) In(x - y) = xy + y³ ; (2) y =

A: As per Bartleby guidelines rule I am answering only first question as other questions are not the…

Q: -2- 0 y = g(x) 4 7 x

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Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1 (2) sech x - 4 tanh x = 1

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Q: multiple of a and c: =b/(n^3) c = b/(1 + n^2) S 1 du au²+bu+c

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Q: Q5: Find for the following functions: dx (1) In (x - y) = xy + y³ ; (2) y = tan³√/cot(7x);

A: Given :lnx-y=xy+y3y=tan3cot7x

Q: dy dx + 4y - e* = 0, dr y(0) = 4 3

A: Given: dydx+4y-e-x=0, y(0)=43

Q: A spherical iron ball 8cm in diameter is coated with a layer of ice of uniform thickness. If the…

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Q: Find the Taylor or McLaurin series for the following functions f(x) = ln(1+x), a = 0

A: According to the question we need to find out the McLaurin series.

Q: 20. The graph of the first derivative f' of a function f is continuous on (-∞, ∞). -2 -1 f'(x) 1 2 3…

A: According to Bartleby guidelines I can only answer the first three sub questions of the given…

Q: find an equation of a plane passing through the given point and perpendicular to the given vector…

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Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin(A) 00 7 A

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Q: Find the shortest distance between the point A (3, 10) and the line y = x + 1.

A: Our Aim is to find the shortest distance between the point A(3,10) and the line y=12x+1 -(i)

Q: Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM. A $124,000 trust is to…

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Q: dw (C): If w = tan x and x = 4t³ + t; Find dt

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Q: Q1/ Solve the following differential Equations. 3- dx +2²= 3x x

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Q: Q2: Solve the following in 7x²+14x+15 (1) f dx ; (x²+3)(x+7)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Answer the following questions for the function f(x)=x√x²+1

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