MATH 16A

Midterm 1 | Spring '17 | Sheng

(a) (3 pts) Find the distance between $(1, 2)$ and $(-3, 5)$.

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(b) (3 pts) Find the value of $x$ such that the distance between $(1, 1)$ and $(x, 5)$ is $5$.

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(4 pts) Find the equation of a circle with center $(-2, 1)$ and the point $(1, 2)$ is on this circle.

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(a) (5 pts) Write the equation of the line that passes through $(-1, 2)$ and $(0, 4)$. (Write the final equation in slope-intercept form).

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(b) (5 pts) Find the equation of the line that passes through $(-3, 4)$ and parallel to the line $4x - 2y = 2$. (Write the final equation in slope-intercept form)

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(c) (5 pts) Find the equation of the line that passes through $(-3, 4)$ and is perpendicular to the line $4x - 2y = 2$. (Write the final equation in slope-intercept form).

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(5 pts) Given $f(x) = \sqrt{x}$ and $g(x) = x^2 - 1$. Compute $f(g(x))$ and $g(f(x))$.

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(a) (3 pts) $\lim_{x \to 1} (x^2 + 3x - 1)$

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(b) (5 pts) $\lim_{x \to 2} \frac{x^2 + x - 6}{x^2 - 4}$

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(c) (12 pts) Let $f(x) = \frac{|x - 4|}{x - 4}$. Compute the left limit $\lim_{x \to 4^-} f(x)$, the right limit $\lim_{x \to 4^+} f(x)$, and decide whether $\lim_{x \to 4} f(x)$ exists or not.

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