Download Midterm Exam 1 Questions - Calculus I | MATH 131 and more Exams Calculus in PDF only on Docsity!
Test 1 Math 131 Spring 2008 September 29, 2008 HPR Part I ( ____/48 points) : No calculators allowed. Directions: Do your work neatly and legibly on the paper provided. Partial credit is given; so, show all your work. Points for each question are given in brackets to the right of the question number. Circle answers. Please let me know if you use the back of a sheet. Write, “On back”.
- [7 points] Find an exact value of
sin( ). 4
- (a) [4] If
sin 2 t
and^ tan t 3 , find^ cos^ t^. (b) [3] What is the value of the angle t in radians?
- (a) [7] State the definition (as a limit) of the slope of the tangent m tan (^) to the graph of the function f(x) at x a (^). (b) [7] Use the definition in (a) to find the slope of the tangent to 4 x^3 2 at^ x^ ^2.
Test 1 Math 131 Spring 2008 September 29, 2008 HPR
- [8] Evaluate 7 7 5 3
lim x 2 36 1 x x x x x
- [8] Evaluate 0
lim x x x
Test 1 Math 131 Spring 2008 September 29, 2008 HPR
- (a) [9 points] consider the function f^ ( ) x^^ ln^ x. In the rightmost column of the table give a value of the slope of the secant through the points (^ x 1^ ,^ f^ (^ x 1^ )) and (^ x 2^ ,^ f^ (^ x 2^ )) for each pair of values x 1^ and x 2^. x 1 x 2 Slope of secant 2 2. 2 2. 2 2. Scratch space. (b) [6] Using the only the values in the rightmost column of the table, select your best estimate of the slope of the tangent to f^ ( ) x^^ ln^ x at x = 2. Justify your answer.
- Use graphical and numerical evidence to conjecture the value of sin lim x x (^) x
(a) [6] Graphical evidence: Draw a neat graph of the function between x=2 and x=4. Use open circles to indicate where the function is undefined.
Test 1 Math 131 Spring 2008 September 29, 2008 HPR (b) [4] Numerical evidence: Give the values of the function for x=. (^) - 0.001 and for x= (^) +0.001. (c) [4] Conjecture: Based on (a) and (b), what is your conjecture about the value of sin lim x x (^) x
- [10] Find k so that the function f(x) is continuous on any interval. f ( x )
x x x kx x
Test 1 Math 131 Spring 2008 September 29, 2008 HPR (b) [5] Considering 0 w 16 , use your graph to give values of w for which f(w) is not continuous. BRIEFLY explain your answer briefly in terms of limits.
