Find dy for given Values OF x and AX y= 4x315x X=-3 and AX = 0.3

Q: 2) Calculate lim ( In(3x + 1) – In(2x + 1)). -

A: Since you have asked multiple questions, we will solve the first question i.e., Question-(2) for…

Q: Use power series to estimate arctan .2 correct within -10-. Leave your answer as a simple fraction…

A: The power series for arctanx is x-x33+x55-x77+..... For a estimate within 12·10-5, we'll have to…

Q: 2x+11 3. 1 dx, evaluate Consider 3 x² + x – 6 = xp dx X+3 X- 2 X+3 X-2 |(x- 2)° +C In x+3 x-2 In +C…

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Q: %3D Determine the speed along a parameterized path c(t) = (6 sin¬'(t), 3 tan¬(1)) at time t = 0…

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Q: S x2 +2x-10 (2x+4) + 1 JE + 4x +5) Consider dx = x² (x² + 4x + 5) (2x+4) + 1 dx- x² + 4x +5 dx ,…

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Q: 22 - 12x dx x?(3x² – 10x – 8) partial fraction is to be employed. What is the most appropriate form…

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Q: 10) For y= vx+8, use the differentialE dy to approximate Ay when x changes from x =1 to x 0.97

A: This question can be solved using the concept of linear approximation.

Q: Compute the derivative of each function. f (x) = e³x* += (cscx + sec x)² %3D %3D

A: Follow the procedure given below.

Q: 7.) Find the area inside the graph of r-7 + 3cos(e) and to the left of the y-axis

A: As per bartleby guidelines we only give first  questions answers.

Q: S, f(2)dx+ f(x)dx = 21. 23. S f(G)dr + J, f(x)dx =, = <p(x)f f – xP(1)f !!

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Q: 3x2 + 7x + 28 A f(x) Using partial fraction, evaluate x3 + x2 + 7x dX, the decomposed fraction is x2…

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Q: 1 y dydx %3D 0. Select one: O True O False 2.

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Q: x² – 1 lim x→1 /x – 1

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Q: 5 Evaluate the integral 2x cos(xy)dydx 4 0.

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Q: 2- oiffemontiake with nespeef fo z and ataking X as a cams fant. he * (2-2a)" y.l00 (2-2x)" (1-0) =…

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Q: 4 Using Trigonometric Substitution x2 +4x - 5 dx = | f(e)de find the new limits of integration. X+2…

A: By using Trignometric Substitution fin the limits∫14x2+4x-5x+2dx=∫abf(θ)dθ

Q: integral

A: We have to choose the correct option from the given options according to the given information

Q: Sketch and use a double integral to find the area of the region R bounded by the lines: y = 0, y = x…

A: Graph of the given fucntions

Q: If R is the region enclosed by x-axis, y = -3x and x = -2, then evaluate the following double…

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Q: give the equivalent cartesian coordinates of ρ = π

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 41. Suppose that both f and g have inverses and that h(x) = (f o g)(x) = f(g(x)). Show that h has an…

A: Explanation of the answer is as follows

Q: Find the area of the region bounded by the x and y axes. The line x = 2. Show your complete solution…

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Q: x e2x dv

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Q: r1/2 x2 dx is F(b) – F(a), where Fla) and F(b) are real numbers. What is the value of F (a)? The…

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Q: What change of variables is suggested by an integral containing * V25 + x²? O a tanø O none of the…

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Q: 4) Equation: 4x +9y² = 1 1 Given that dy/ dt =8, find dx / dt when (x,y)= 3 9

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Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = x°e=x (a) Find the…

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Q: A clothing manufacturer has the marginal profit function MP(x) = 40 - 0.02x, Os xs 100 (in dollars…

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Q: Evaluate sin*(2x)dx. sin (2x)dx. sin 4x, sin 8x + C 64 3x 8 8. sin 8x + C 64 O X sin 4x 4 8 8 O 3x +…

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Q: Direction: Find the integral of the following functions: 1. S(5 cos x + 7 sin x) dx 2. S(3tan2…

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Q: 5. Let ƒ be a function satisfying the following properties: lim f(r) = 2 continuous on R \ {0} •…

A: a. Here, we have  limx→0-fx=-∞, which means the function has a vertical asymptote x=0; limx→+∞fx=0…

Q: S csc6 cot* w dw W

A: Given,           ∫csc614wcot414wdw

Q: 1. Find (sin?) A 2 sin z cos a x* B 2 sin r" coS T* 1²-1 1. C 2 sin r? cos T² r² Inr D 2 sin r*…

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Q: Find the derivative of y with respect to t. y = In (t) dy %3D dt

A: Given function y=lnt9 we have to find derivative of y with respect to t. ln is natural logarithm…

Q: _12. What is the maximum directional derivative Daf of the function f(x,y,z) = x – y² + z² at the…

A: Let's find.

Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: A continuous function y f(x) is known to be negative at x = 2 and positive at x=7. Why does the…

A: Given that f(x) is a continuous function.

Q: Does this mean the sequence is always convergent?

A: We can take limit of the sequence.  limn→∞an=limn→∞-1n-1nn+n

Q: 1) Hs] Solve the IVP: y" – 8y + 16y = 0, y(0) = -3 and y (0) = -1. %3D |

A: Use homogeneous differential equations to find solution.

Q: (7) If 4.5* = 97, an approximate value of x is (A)x = log(97) × 1.987 (C) x = In(97) z 4.575 (B)x =…

A: 7.    4.5x=97 Note:      Multiple questions are given, we are answer with only one question. if you…

Q: Given: dx x3 Using trigonometric substitution, solve for the integral form in terms of 0.

A: This question can be solved by taking x=3secθ

Q: 3x² +7x+28 f(x) x2 + x+7 A Using partial fraction, evaluate x3 + x2 +7x aX the decomposed fraction…

A: The objective of the question is evaluate the indefinite integral in partial fraction.

Q: dy Find dx for the curve: x = t, y= 2/t, t>0

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Q: A.) In each of the following, find the area bounded by the given curves; Solve for the points of…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given,   r(t)=cos(πt)i-ln(t)j+t-16k

Q: How can you relate antiderivatives as an opposite of derivatives in your life? explain

A: Solution is given below:

Q: Integration by Parts Example 4. Evaluate In x dv,

A: The given integral is: I=∫lnxdx   As we know that; ddxlnx=1x

Q: Evaluate the iterated integral: e dydx

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Q: Find an equation for the tangent line to the curve at the given point. Then sketch the curve and the…

A: Given: y=8x, 16,32

Q: k! (ii) ek k=1

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…