Complete the following statement. If dy/dx is large, then small changes in x result in relatively ________ changes in the value of y.

Q: d(a*) Suppose a E R, where a>0, a± 1 What is dx

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Q: Evaluate d/dx cot x

A: Our Aim is to compute the derivative of cot (x).

Q: Complete the following statement. If dy/dx is small, then smallchanges in x will result in…

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Q: Evaluate each of the following below. 2. dx

A: The given integral is ∫1∞1x3dx. Evaluate the integral ∫1∞1x3dx as shown below.…

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Q: FIND DY/DX OF THE FOLLOWING 4. y= cot (1+e)

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Q: Which of the following functions is a solution of the exact equation? (6x + 4y)dx + 4xdy= 0.

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Q: Find if y = In (9x² + 8y). dy dx

A: Solution is given below

Q: dx |

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Q: dx Find the value of if it exists. x2 – 1 1 8.

A: I=∫1∞dxx2-1=∫1∞dxx+1x-1=12∫1∞2dxx+1x-1=12∫1∞x+1-x-1x+1x-1

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A: Fact :- Sum of squares is always non negative

Q: and du = dx L dx = , we need to set u(x) = x-1 (x-1)

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Q: S tanx It Cosuy dx

A: Topic:- application of integration

Q: Determine the following. 3x dx

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Q: Q10 Monday, March 1, 2021 8:30 AM Q10) Find dy/dx if:

A: To find out dydx=ddx(ln((x+1)5(x+2)20))We can write the equation in exponential form;…

Q: find x for which = 0. dx

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Q: Solve the following Bernoulli equation: dy - 4y-2y dx

A: We have to do variable separation.

Q: Solve the following D-E 1) xdy + ydx = x³y® dx

A: First divide dx both sides.

Q: 2. Find S x?e* dx.

A: topic - integration

Q: Evauate the below 1 dx 4+5cos x

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Q: L {t?cos t}.

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Q: For each of the following y, find the d^2y/dx^2

A: We know, d/dx (xn)= nxn-1, for any real number n. d/dx(u(x)v(x))= v(x)*d/dx(u(x))+u(x)*d/dx(v(x))

Q: у +x")dx — хау 3D 0

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Q: Determine dx, assuming x > 0. [3 points] Hint: This can be rewritten 10. as dx.

A: We can use the method of substitution in order to solve the given problem.

Q: _5. 2/xy = 3 ху

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Q: Find the given derivative. 6. D,5x D.5x

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Q: Q1) Solve the following ordinary differentiai eyilation: (x + y)dy = dx

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Q: et Evaluate dx using an appropriate substitution. 1+ e2x a

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Q: 2x exp Evaluate dy dx y? ,2 Check Answer

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Q: Find the following

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Q: dy/dx

A: We will perform implicit differentiation.

Q: Show that e* dx e

A: To Prove,∫1∞e-xdx = 1eConsidering LHS, let LHS be y - y = ∫1∞e-xdx…

Q: If xy + ey = e, find the value of y′′ at the point where x = 0.

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Q: At which of the five points shown on the graph are and dx dy both positive? dx2 E В

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Q: et? et? dx + dx = dx

A: Use the integration form, ∫acf(x) dx=∫abf(x) dx+∫bcf(x) dx

Q: Determine if the equation 2xy dx + xy dy = 0 is exact. Identify M =O and N=O

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Q: dy if: dx g coth =

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Q: Derive a formula for the equation below: хп In x dx Where a.) n =-1 b.) n + -1

A: We use  the substitution method and integral by parts for each of the cases given. Note that…

Q: 1 dx (2x + 1)'

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Q: Solve the following by indicating the steps and describe the process: sinx dx SCOS² 1.

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

Q: If xy + e = e, find the value of y" at the point where x = 0.

A: First find y corresponding to x = 0 than take derivative of the given equation two times and put the…

Q: If dx is between 3 and 6, then c must be between..

A: If ∫0c1x3dx is between 3 and 6 , then c must be between

Q: | (3e* + 1)? e* dx

A: Given integral, ∫3ex+12ex dx

Q: Calculate dy dx.

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Q: bx a a dy dx

A: Our Aim is to evaluate the integral given below:-∫0a∫0bxady dx -(i)

Q: a. Find dy dx of the following. 1. y = (3x? – 2x + 7)49

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Q: B D 3. d²y and -both dx? dy 1. At which of the five points on the graph in the figure above are dx…

A: Given, The graph between y and x  Fiven points A,B,C,D,E  are given on the graph