Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval -2, 5 is 4 and L (8f(x)+ K) dæ = 34, where K is a real number. Calculate 3K.

Q: Estimate how much the function f (x) = 1/1 + x2 will change if x decreases from 1 to .9.

A: Given: The function  f(x) = 11+x2 To find: How much the given function will change if x decreases…

Q: Find the intervals where f(x) = x2e−x is increasing and where it is decreasing.

A:

Q: Suppose f is a function with f(16) = 23 and f '(16) = 2. Estimate the following values of f. f(13)=…

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Q: For what numbers 0 is f(0) = csc 0 not defined?

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Q: 71. Is the function given by g(x) = 4x - 6x continuous on R?

A: To check whether the function g(x) is continuous on ℝ. The given function is gx=4x3-6x Also, the…

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: Is the function below continuous at x = -5? f(x)=x3−2x2+5x+1

A: We are to simplify

Q: Consider the piecewise function 1 3.x if x < -2 f (x) = ax2 + 2x + b if – 2 < x Where a and b are…

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Q: d) Find the value of the constants ' a’ and b ’ that makes the function continuous at x= 3 ах + b ;…

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Q: What is the length L of the interval on which the function f(x)=x4e−x is increasing?

A: Given

Q: Determine whether f is continuous at a = -1.

A: Given- fx=x2-1x+1   if x≠-16           if  x=1 To find- whether f is continuous at x=-1 or not.…

Q: Excrcise 10. Find the derivative d -7x * [" (t³ + 2) dt dx

A: Given,          ddxx∫57xt3+2dt

Q: Where is Log(z2 + 2) holomorphic (Analytic ) function ?

A:

Q: Find the value(s) of "c" that satisfy the conclusion of the Mean Value Theorem for the derivative of…

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Q: Which derivative of f tells us whether the function is increasing or decreasing?What do we check to…

A: Given function ,  f(x) = ln ( x2 + 2x + 5)  Find interval of increasing and decreasing .

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: