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Calculus

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Q: Verify the MVT for f (x) = ln x on [1, 4].

A: f(x)=lnx is continuous in the interval [1,4] f'(x) = 1/x is also continuous on (1,4) So f(x) satisf...

Q: Two quantities increase exponentially with growth constants k = 1.2 and k = 3.4, respectively. Which...

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Q: Use any method to evaluate the integrals in Exercises 63–68. sec³ x 63. sin' x - dx cos“ x dx tan x ...

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Q: Find the dimensions of the box with square base with: (a) Volume 12 and the minimal surface area. (b...

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Q: Find the derivative of the function by using the Quotient Rule. Simplify your answer. f(x) = x ...

A: Consider the given function

Q: 60. The geometric, logarithmic, and arithmetic mean inequality a. Show that the graph of e* is conca...

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Q: Find the derivative of f (x) = 2e". f' (æ) =

A: Given function

Q: Find the equation of the tangent line to the curve y=x^4+2e^x at the point (0,2).

A: Consider the given curve y=x^4+2e^x

Q: Sketch the graph of y = x2 − 5x + 4.

A: Given equation: