Find the complete solution of e sinx- - Note: fe" du = e" + C dy cos² x=0. dx

Q: y = x^ (Hint: First take LN of both sides and use implicit differentiation.)

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A: The given integral:∫x2+2x-2x2-2x+2dx

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A: Topic:- application of integration

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Q: - nsider the function f(x) = 2x³ + 3x² – 36x - 54. a. Find the first derivative. f'(x) = b. List any…

A: Topic:- calculus Note :- as per our guideline if more than three subparts posted than only first…

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A: We have doing solution useing logarithm laws

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A: We can solve this as follows:

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A: Given; x=y^2-y-6, x=2y+4

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A: The given summation,         ∑j=11nj+22

Q: I. Find the sum of the following convergent series. lim = 348 lim lim 846 Σ [tan² (2n-1) - tan²¹…

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Q: 3. Given that 2 = 6²¹ sin (u + ), e2v Use chain rule to find az/0x when x = 0, y = 0. u=e¹ - sin (y…

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Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

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A: The given integration is: I=∫cos2y1+sinydy   We know the common integral. ∫sinxdx=-cosx+C

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Q: Consider the system: a) show that [3t+4] =-2t+1 4 Z t-1 b) golve (*) with the initial condition.…

A: Solution

Q: If you evaluate the integral expression Blank 1 Add your answer 2x-1 - 3|dx the result is Blank 1…

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Q: Consider the sequence -13, -3, 7, 17,.. 10n + 7. ...9 a. How many terms are there in the sequence?…

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Q: entus 1. √ √2x + 1 dx

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A: topic- definite integral

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Q: Scanned with CamScanner 10.f cota y sec y dy

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Q: X X-2 such that (fog)(x) = x + 2. Q₁/ let f(x) = , find a function y = g(x)

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

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A: We have to find the gradient field.

Q: Consider the function f(x) = 4xe-x². Identify the locations where f has transition points. (Give…

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Q: In evaluating x=3.98. dx x²-9 is same as evaluating lim (In(f(x))). Determine the value of f(x) if…

A: First we evaluate f(x) using substitution

Q: f(x) = -x² + ax + b, x < 2 (-ax + 7, x ≥ 2

A: Here we have to find the value of a and b such that,  f(x)=-x2+ax+b, x&lt;2-ax+7, x≥2 is continuous…

Q: Given than [ f(x) dx = 7 and S. -2 (A) [₁ f (x) dx - [³ f (a) dx = -10 B) None of the given choices…

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Q: Question 2 Iff and g are continuous on [a,b], then t True B) False in √ [f(x)g(x)]dx = {√°f(x)dx)(√°…

A: Given that f and g are continuous function on [a,b].

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Q: 11.J sin 3 x sin 6 xdx 3

A: To evaluate the given integral.∫sin 3x sin 6x dx

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Q: Evaluate x ds, where Cis с a. the straight line segment x = t, y = = 737₁1 3' b. the parabolic curve…

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Q: For the function y =f(x), it was found out that f"(c) = 0. What can be said that x=c? O critical…

A: We can find the answer as below.

Q: -1 (a) cos (b) log5 (25) -√√3 2

A: Solved below.

Q: Solve for the derivatives of the following functions with complete solutions. a. y = ln (5x²) b. y =…

A: Answers provided by you have mistakes only (c) and(d) matches.

Q: Using Simpson's method spaces) √²x² dx for n = 4 is equal to Blank 1 (use 2 decimal places with…

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