Math 5A, calculus, Mrs. Badalyan FINAL EXAM 6/8/20, 7:45-9:45 pm. ONLINE Print Name_________________
pg. 1
Show your very detailed work. Do not skip any part of the problem. Show all justifications of your
conclusions and answers. Be as accurate as possible not to miss any points. Please be advised it is
limited to two hours only.
1.(10pts) Find the numbers at which function f is continuous if any, at which it is continues only from
the right, from the left, or neither. Clearly graph the function in the space provided. Justify your answers
by checking all three criteria for continuity. Make your conclusion based on those three criteria clear and
underlined. =
22−7+3
−3 , − 2 ≤ < 3
6 − ( − 4)2, 3 ≤ < 6 −2 + 14, > 6
2.(5 pts) Find the limit lim →0
1−√1+3
3(5 pts).Find
:
tan( − ) =
1+2
Math 5A, calculus, Mrs. Badalyan FINAL EXAM 6/8/20, 7:45-9:45 pm. ONLINE Print Name_________________
pg. 2
4. (5 pts) A particle is moving along a hyperbola xy=8. As it reaches the point (4,2), the y-coordinate is
decreasing at the rate of 3 cm/sec. How fast is the x-coordinate of the point changing at that instance?
Sketch the graph.
5. (4+1 pts) 5a.Find the derivative of = cos2( 3 − 5)2. Simplify as much as possible.
5b. write the equation of the tangent line to the point (5/3,1).
6. (5 pts) Find the point on the curve = √, ℎ ℎ (3,0) Sketch the graph, Verify
that you found the extreme point.
7. (5 pts) Find the derivative of the function = ∫ cos
3+1 √ + sin
8. (5 pts) Set up and do not evaluate. Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified line. Sketch the region, by
finding x and y intercepts, HA and VA asymptotes (no limits are required). Show
the slicing, indicate the method you are using. = , = 2
1+3 = −1
Math 5A, calculus, Mrs. Badalyan FINAL EXAM 6/8/20, 7:45-9:45 pm. ONLINE Print Name_________________
pg. 3
9. (5pts) Evaluate. Use the washer method to find the volume generated by rotating the region bounded
by the given curves about the specified axis. = √, = 2, = −3
10. (10 pts) Graph the function = 1 + 1
+
1
2 Clearly indicate domain, VA (use the
limits),HA( use the limits), first derivative, state the Intervals of
increase decrease, extremes; second derivative, intervals of CU/CD,
IP. Provide a detailed graph.
