For each given functions, find the slope of the tangent at a given point using first principle definition. a. y=x^(3)+8  (-2,0) b.y=2x^(2)-(5)/(x+2)  (0,-5/2) c. y=\sqrt(x)  at x=9

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A: Solution: The train..........at 12 PM

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A: The solution is given in the next step.

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Q: lim X→+∞ 5 In³ x 2 X²

A: Let's evaluate limit.

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Q: Evaluate the integral: fe* sinhxdx. Select one: O a. -+C 0b. ²+0 ++ C d+C

A: We can solve this as follows:

Q: Solve the system of differential equations. = - X1 6x1 + 2x2 X2' - 2x1 - 10x2 2, x₂(0) - 22 = x1 (0)…

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Q: Practice Problem Instruction: Find the coordinates of the midpoint of a segment with the given…

A: This is a problem related to midpoint of the line segment. based on the general formula and concept…

Q: 5. Find the limit using any method of choice. x + 2 lim x-2 2x² - x - 10

A: A detailed solution is given below.

Q: TYPEWRITTEN ONLY PLEASE. ILL UPVOTE ONLY IF TYPEWRITTEN, COMPLETE, AND CORRECT. DONT ANSWER IF YOU…

A: To differentiate the functions.

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A: Given

Q: Find the curvature K and the radius of curvature R at (1,2). (A K= √/2. R=₁ R = √2 (В) K= R= 2√2 2√2…

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A: The given problem is solved below in detail.

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A: Here, note that the function ln1000x grows asymptotically slower than the polynomial x5.

Q: f cot x dx Select one: a. In sina+c + c + c + c O b. In sec x oc. In csc r od. In cos x

A: cotx = cosx/sinx

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A: Ths question can be solved using the formulas of Laplace transform.

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Q: d. lim+ In 1000 X X5

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Q: 2 2 dx 2x (V2x + 9)

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A: Given

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Q: 3 fin [ ха Txx² 2 - 1/2 to

A: To evaluate: ∫13lnx21+x212dx=∫1312lnx21+x2dx=12∫13ln x2-ln (1+x2)dx=12∫13(2ln x) dx-12∫13ln(1+x2)…

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Q: Sº₁ 1 2 x³ dx x²+x+1

A: Solution of given question is written in below steps.

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Q: 4) (1, 150°) 120° 150° 180° 210⁰ 240 90° 270⁰ 60° 2 3 300⁰ 30° 4 330⁰ Ꭴ

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Q: 1 x² dx So √4-x²

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Q: Find the length of the are of the function x² = 4y from x = -3 to x = 3.

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Q: Find Value of integral ) dx X+1

A: Given query is to find the value of the integral.

Q: 5. Find the limit using any method of choice. x + 2 lim x-2 2x² x 10

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Q: Find the area of the region bounded by the curve y=x^2-3x the x-axis and the lines x = 1 and x = 2.

A: This question is based on application of integration.

Q: √² (5x²-3x+18) dx 9x - x³

A: Integration is done by dividing polynomial.