Your submission must be a single PDF and all pages must be oriented correctly (e.g. pages should not be upside down). If your submission does not follow these guidelines, then

points may be deducted. Please answer each question fully, providing all reasoning. You will be graded based on both mathematical correctness and clarity of writing. See the Written Portion Rubric on D2L for more details. Let b denote the last nonzero digit of your UCID number. e.g. if your UCID is 9876543280 then b = 8. 1. Let C and D be constants. Consider the function f(x)=\left\{\begin{array}{ll} \sqrt{b x+1}+C, & \hat{x} \geq 0 \\ D x+x^{4} \sin \left(\frac{b}{x}\right), & x<0 \end{array}\right. Use the limit definition of the derivative f^{\prime}(a)=\lim _{x \rightarrow a} \frac{f(x)-f(a)}{x-a} to determine what C and D must equal in order for f(0) to exist. (You must use the limit definition of the derivative to receive credit for this question. If you do not, then you will not receive credit.) Hint: You will need to use one-sided limits.