The limit below represents the slope of a curve y = f(x) at the point (a,f(a)). Determine the function f and the number a; then calculate the lim 2(3+h)-- - 162 lim h→0 h

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A: Please refer to the image below

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Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: topic - application of derivatives

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Q: Given: parametric curve H defined by r(t) = tan-¹t and y(t) = eªt, where t = R (a) Find the slope of…

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Q: Calculate the integral approximations To and M6 for 10 x³ dx. Your answers must be accurate to 8…

A: ∫ab f(x) dx≈Tn=∆x2fx0+2fx1+2f(x2)+...+2f(xn-1)+f(xn) ∫ab f(x) dx ≈Mn=∆xfx¯1+fx¯2+...+f(x¯n) ; where…

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A: Given, ∫01w36w4+3dw

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A: solution is given below

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A: *Formula:- 1. ∫exdx =ex.2. sinxcosx = tanx.3.  1cosx = sec(x).4. ∫sec(x)tanx = sec(x).5. ey =x ⇒y =…

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A: Solution is done in step 2

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A: Find the equation of tangent line and normal line to the curve y=2x-1 at x = 5.

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A: Follow the procedure given below.

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Q: Q1: convert the Integral 1-X fydx to the polar coordinates.

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Q: In evaluating dx , is same as evaluating lim (In(f(x))). Determine the value of f(x) if x=4.6. C-3+…

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Q: 8. For what value of the constants A and B is the function f continuous on (-∞, ∞)? Ar + B for x 2…

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim x x→0+

A: We have to determine limit by useing l hospital rule

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Q: Solve f(x + 1)(x + 2)²(x² - 1)dx with and without the even-odd theorems (show both solutions).

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A: Let the radius of the cylinder is = r and the radius of the sphere = R  Let the height of the…