Find dy/dx. x=tsin(t), y = t² + 5t

Q: Part b pls

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Q: find either lim 5x3 x→∞ ex one that takes less time!) Find lim (1 +5)* X→∞ 5x3 x→0 ex-1 or lim using…

A: As per the rules we are supposed to answer the first question and rest can be reposted.

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A: I=∫cosxxdxwe know that  ∫cosxdx=sinx+cdxndx=nxn-1

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Q: (iii) Does n³ e" n=0 converge absolutely, converge conditionally, or diverge?

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A: From the figure center = ( -4 , 2 ) let r = radius

Q: Find using implicit differentiation. 하 경기 = dx dx 2x3 = 3y2 + Ty

A: Please see the below picture for detailed solution.

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Q: Write a formula for the nth term of the following geometric sequence. Then use the formula for an to…

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Q: Determine the slant asymptote of the graph of f(x)= x²-8x+14 x-3 Write your answer in the format y =…

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Q: bounded by the following curves: y = x³/2, y = 8, x = 0, y = 0. Find the volume of the solid…

A: Given ,       y = x32 ,  y=8  ,  x= 0 , y=0.  From Shell method-     Since the revolution is around…

Q: an+1 Find the first six terms of the sequence defined by a₁ = 1 and 5 = an + 1 for n ≥ 1

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Q: What is the Remainder R, when ƒ(x) = is divided by (x + 1)? 20 16 22 30 30 4x³ + x² - 3x + 2 3 =…

A: To find the remainder

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Q: (c) sin 13л 15 COS Зл 15 COS 13п 15 sin 3п 15 Answer: sin 10п 15 = sin (2) 3 2п √√3 =

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Q: 2x + 1 [20+1 0 1 dx = ln |x| − 2 ln x + c O 2 ln |x|ln |x²|+c 2 ln x 1 X + c 1 ○ In |x| - = - + c x

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Q: Suppose that a rectangular box has a volume of 18 cubic meters and is being expanded in such a way…

A: Given: A rectangular box has a volume of 18 m3 and is being expanded in such a way that its length…

Q: Find all complex solutions of 3x+6x+1=0. (If there is more than one solution, separate them with…

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Q: Sketch the region enclosed by y = e³, y = e¹x, and x = 1. Find the area of the region.

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Q: Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index…

A: we know that  numretor and denomintor are the sum of consecutive numbers given…

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Q: The length of arc of the curve given by the parametric e x = t³, y=t², -2≤ t ≤0 is given by to A dt

A: given curve is :-x = t3         ,                y = t2 and     -2≤t≤0then we have to set up…

Q: 38. Simplify: cos 40° cos 110° - sin 40° sin 110⁰ 39. Simplify: cos 50° cos 20° + sin 50° sin 20⁰

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Q: 1. Given the equation y = -7cos(4x + 20), find the following: (write the answers here and on paper)…

A: To solve the following problem and find the following things

Q: - After finding the critical values of f(x, y) you compute D(x, y) = fxx fyy – fxyfyx and evaluate…

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Q: Use Variation of Parameter to find a particular solution for y"-4y'-12y=x

A: The given differential equation:y''-4y'-12y=xWe need to find the particular solution using variation…

Q: The graph of one complete period of a cosine curve is given. y 3 f (a) Find the amplitude, period,…

A: We need to find equation of curve.

Q: Use Calculus to find the behavior of g. g(x) = x³ 3x²is restricted to the intervalr € [1,4] 19. g(x)…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

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Q: O A. No, since we have only shown that Sk+ 1 satisfies the statement. OB. No, since we must show…

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Q: Given the geometric sequence: 22, 88 352 " 15 225' Find a10 = ... Find an explicit formula for an,…

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Q: 9) The sequence a₁ = a) Diverges b) Convergest c) Converges to 15 2 d) None of the above 4n²+1

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Q: Consider the indefinite integral a) This can be transformed into a basic integral by letting U = du…

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Q: For the function f(x) = 4x 4x -4x+8, f

A: Given: f(x)=4x4-4x3-4x2+8

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A: We need to fid function from graph.

Q: Obtain the general solution of the D.E. y - 4y + 4y=e²x O 1 + y=c₂e²+ = x²e² O 1 2x y=₁₁²³² +₂²² + =…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the point (, ).…

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Q: 22. g(x) has an inflection point(s) at:

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Q: Let (u, v) be the inner product on R² generated by A = 1=[ A and let u = (3,-4), v = (-4,5). Find…

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Q: The given figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 26…

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Q: Include several decimals for accuracy when the problem is graded. - 1)" 200 nº.8 ∞ n=1 S4 = error

A: To solve the following series problem

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: Here,              We have given a definite integral and  we have to solve it by using mid point…

Q: 469 2 sin+sin 0 tan²0 de sec²0 S

A: Given query is to find the integral.