Use Rolle’s Theorem to show that the equation ln(1 + x 2 ) + 2x =...

Use Rolle’s Theorem to show that the equation ln(1 + x 2 ) + 2x = 0 has at most one solution. Provide a full explanation, justifying each step in your argument.

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milcah answered 2 years ago

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a =...

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. Lf (x) = Lg(x) = Lh(x) = (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain. The linear approximation appears to be the best for the function ? f g h since it is closer to ? f g h for a larger domain than it is to - Select - f and g g and h f and h . The approximation looks worst for ? f g h since ? f g h moves away from L faster...

Use the factor theorem to show that x+2 is a factor of f(x). The find all...

Use the factor theorem to show that x+2 is a factor of f(x). The find all real zeroes for the polynomial given that x+2 is a factor of f(x). f(x) = x^3 -5x^2 -2x +24

This problem refers to the Mean Value Theorem, using f(x) = −x 2 − 2x +...

This problem refers to the Mean Value Theorem, using f(x) = −x 2 − 2x + 3 on the interval [−2, 1]. (a) Does the Mean Value Theorem apply to f(x) on the indicated interval? Explain why or why not. (b) Find the (x, y)-coordinates for the endpoints of the function on this interval and calculate the slope of the line through these points. (c) According to the Mean Value Theorem, what would f'(c) be equal to? (d) Determine a...

On what interval(s) is the function f\left(x\right)=2x-\ln\left(3x^2\right)f(x)=2x−ln(3x 2 ) both decreasing and concave up? You will...

On what interval(s) is the function f\left(x\right)=2x-\ln\left(3x^2\right)f(x)=2x−ln(3x 2 ) both decreasing and concave up? You will only earn credit by showing your work algebraically (applying Calculus).

show that the equation 2x+2 cos x+5=0 has exactlly one real root

Find an equation of the tangent to the curve x = 2 + ln t, y...

Find an equation of the tangent to the curve x = 2 + ln t, y = t2 + 4 at the point (2, 5) by two methods. (a) without eliminating the parameter (b) by first eliminating the parameter

How do you show that the function "f(x) = {[x-1;x<2], [2x-3;x>=2]}" is not differentiable at "x=2”?

1. Find the equation of the line tangent to the curve y=2x^2 + sin4x at x=...

1. Find the equation of the line tangent to the curve y=2x^2 + sin4x at x= π/3. 2. Determine the point(s) where the tangent line to y= 2sinx-4x has a slope of-3 in the domain 0≤x≤ 2π. b) Find the equation of the tangent line.

1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 =...

1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 = 0 (a) Convert the equation into a first-order system in terms of x and v, where v = dx/dt. (b) Find all of the equilibrium points of the first-order system. (c) Make an accurate sketch of the direction field of the first-order system. (d) Make an accurate sketch of the phase portrait of the first-order system. (e) Briefly describe the behavior of the first-order...

1114) intg{ 2x ln(x^2) dx } = (Ax^B)*(ln(x^2)+F) + C. Determine A,B,F. ans:3 1130) Evaluate intg_9_17{...

1114) intg{ 2x ln(x^2) dx } = (Ax^B)*(ln(x^2)+F) + C. Determine A,B,F. ans:3 1130) Evaluate intg_9_17{ (x^2 - 4x + 7) dx }. ans:1 1132) Integrate from 3 to 7 the function: ( 1 / (x^2 + 9x) ). Calculate a floating-point value. ans:1

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