Practice 10 questions on MA100 - MA100 Mock Final Exam at Mathematics & Statistics Learning Support. Free AI-generated quiz on uNotes — track your score, retake anytime.
2Evaluate the limit: $$ \lim_{x\rightarrow 5} \frac{3- \sqrt{x+4}}{x-5} $$
3Determine all, if any, horizontal asymptotes of the function $$ f(x) = \frac{4e^{2x} - 5}{3+ e^{2x}} $$
4For the piecewise-defined function $$ h(x) = \begin{cases} kx+5 & \text{if } x < -1 \\ l & \text{if } x=-1 \\ 2k-4x^2 & \text{if } x>-1 \end{cases} $$ determine the values of $k$ and $l$ for which $h$ is continuous at $x = -1$.
5A moving object's position is given by $s(t) = (t - 4)^2 - 6$. Determine the instantaneous velocity of the object at $t = 3$ seconds.
6Determine the derivative of the function: $g(x) = x^2 \log_4 (3 - x)$.
8Determine the equation of the tangent line to the curve $$ \cos(x - y) = y e^{x^4} - \frac{\pi}{2} $$ at the point $(x,y) = \left(0, \frac{\pi}{2}\right)$.
9The length of a species of fish at time $t$ (in months) is given by $L(t) = 34 - 32(k^t)$. If $L(4) = 10$, find the value of $k$.
10Consider the function $f(x) = \frac{10 \ln x}{x^2}$. Given that $f'(x) = \frac{10(1 - 2 \ln x)}{x^3}$, determine the intervals on which $f$ is increasing and those on which $f$ is decreasing.
