Exam Hub Rendering Issues

get a hint

hint

This statement is correct. For Rolle's Theorem to apply, the function must indeed be continuous on the closed interval $$[a, b]$$ and differentiable on the open interval $$(a, b)$$. These conditions ensure that the function does not have any breaks, jumps, or sharp corners in the interval, which are necessary conditions for the existence of a point $$c$$ where the derivative $$f'\(c) = 0$$.

This statement is correct. For Rolle's Theorem to apply, the function must indeed be continuous on the closed interval $$[a, b]$$ and differentiable on the open interval $$(a, b)$$. These conditions ensure that the function does not have any breaks, jumps, or sharp corners in the interval, which are necessary conditions for the existence of a point $$c$$ where the derivative $$f'\(c) = 0$$.

renders the first three latex in the editor but not in the rendering

Which of the following is the correct antiderivative of $\frac{1}{\sqrt{x}}$?

Square roots aren’t rendering properly in the editor

Rank the following functions in order of increasing difficulty to differentiate using the chain rule: $$f(x) = (3x^2 + 2)^5$$, $$g(x) = \sin(5x^3)$$, $$h(x) = \e^{2x^2 + 3x}$$, $$j(x) = \sqrt{4x + 1}$$.

The one \e messes up everything when actually it could render a lot better

Given the function $$y = \sqrt{x^3 + 3x^2 + x}$$, rank the following steps in the correct order for applying the chain rule to find $$dy\dx$$: A) Differentiate the outer function, leaving the inside function alone, B) Multiply by the derivative of the inside function, C) Identify the inside and outside functions, D) Simplify the derivative expression.

Again renders the first one and semi renders the second but doesn’t work for either term on rendering

I. The definite integral $\int_{0}^{\pi} \cos(x) dx$ equals 0.

II. The definite integral $\int_{1}^{2} (3x^2 + 2x + 1) dx$ equals $\frac{17}{3}$.

III. The definite integral $\int_{-2}^{2} x^3 dx$ equals 0.

Which of the following statements are true?

new lines dont render in rendering but do in editor

The introduction of mechanized production has revolutionized the textile industry, making production faster and more efficient. However, this advancement has not come without its costs. Many skilled artisans have found themselves out of work, unable to compete with the speed and low cost of machine production. The social fabric of our communities is being torn apart as traditional crafts and trades disappear. It is crucial that we find a balance between embracing new technologies and preserving the livelihoods of our skilled workers. Perhaps, through education and retraining programs, we can ensure that the benefits of mechanization are shared by all.

William Morris, News from Nowhere, 1890

asdf