Show that(1++)´-as x → ∞,→ e.HINT: Since the logarithm function has derivative 1 atx = 1,In (1 + h) – In 1In (1 + h)→ 1.as h → 0,hh

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Answered: Show that (1+:)'→e. as x → o, → e.…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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2. Complete each statement by placing the correct word into each blank. Use appropriate vocabulary and notation. a) This non-zero function in the form y = f(x) has the property : y = y'=y". b) At the point where x = 1, the function f(x) = x³ – 2x² − 3x is and (increasing / decreasing) (concave up or concave down). c) The instantaneous rate of change of a function at a point where x = a corresponds to the slope of the be found by evaluating the at that point and can of the function at that point.
Answer the following showing your proofs
What is the derivative of the exponential function a x, a >0 and a ≠ 1? What is the geometric significance of the limit of (ah - 1)/h as h--> 0? What is the limit when a is the number e?
Q8: Find the second derivative of the function: f(x) = x2 + e* +1 Select one: f"(x) = 3 + e* a. O b. f"(x) = 2x + e* + 1 c. f"(x) = 2x +e* с. O d. f"(x) = 2 + e*
B,c,d,e,f thank you !
Suppose the first derivative of a function is f'(x) = (x- 30)(19x+ 1). The function f is decreasing on:. Enter a comma-separated list of open intervals only. No union symbol. Round parentheses only. All numbers must be exact. Use the symbol o if necessary.
if x + 0bodton a nen 6. Let f(x) = 1 1 if x = 0 Find f'(0).
EN1093 Q2. a) Find the 5th derivative of xʻsin4x (hint: it is simplest to use Liebnitz's theorem) b) There is a cylinder with the radius r = 50 cm and the height h = 150 cm. Estimate the change in the volume of the cylinder if the radius decreases by 5 cm and the height increases by 10 cm, based on the Taylor's Theorem. (Note that the volume of a cylinder V = ar?h) The electricity cost of a building equals to the fuel cost of a local diesel generator and the cost of importing electricity from the bulk power grid, expressed by c) C(Pg, Pc) = a + bP, + cP? + dP3 + pPg where C is the electricity cost of the building; P, is the power generation of the local diesel generator; Pc is the amount of electricity imported from the bulk power grid; a, b, c and d are constant fuel cost coefficients; p is the constant electricity price of the bulk power grid. Find the quadratic approximation near the point P, = 20, Pc = 10.

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Show that (1+:)'→e. as x → o, → e. HINT: Since the logarithm function has derivative 1 at x = 1, %3D In (1 + h) – In 1 In (1 + h) → 1. - as h → 0, h