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Exercise
Find each of the following limits if they exist.
1. x 2 16
x2 4x 2. lim 3. x2 9
lim 2
x x 3 x 4. Find f '( x ) when f ( x ) 5e3 x x 4 2 a. lim f ( x) b. x 3 c. lim f ( x) d. x 3 e. lim f ( x) x 1 lim f ( x) x 3 lim f ( x) x 4 5. Differentiate f ( x ) ln(7 3x) 6. Find an equation of the tangent line to the curve y x 2 3x 5 at the value x = 1. 7. Find 8. Find f '( x ) when f ( x ) 4 (1 3 x 2 )3 9. Find dy
x 4 3x
when y dx
5x 6 3
2
dy
when y ln x8 3e 2 x 3 x 5
dx Find the requested parts below and then sketch the graph of the following function.
YOU MUST SHOW COMPLETE WORK FOR CREDIT. IF YOU SIMPLY FIND
THESE ANSWERS WITH A CALCULATOR AND DO NOT HAVE THE WORK TO
SUPPORT THEM, YOU WILL NOT RECEIVE CREDIT.
y x3 x 2 8 x
10. Intervals where the function increases: Intervals where the function decreases: 11. Intervals where the function is concave up: Intervals where the function is concave down: 12. dy
d2y
Use implicit differentiation to find
and
using the equation 5 x 2 4 y 2 8 .
2
dx
dx 13. 1 7
Evaluate 3t 5 t dt .
9 14. Evaluate x 1 e 15. Evaluate 8 5x dx . 16. 5x
Evaluate 4 xe dx . 17. Evaluate 18. Evaluate the integral: 8 x 2 16 x 5 dx . Assume x 0 when ln x appears. x7 x( x 3)dx . 6 3 (7 x 4)dx 3 3 (9 x 2 e x )dx 19. Evaluate the integral: 20. Find the area of the region enclosed by the curves y x 2 3 and 21. In studies for a medication, 7 percent of patients gained weight as a side effect.
Suppose 761 patients are randomly selected. Use the normal approximation to the
binomial to approximate the probability that 0 a) Exactly 61 patients will gain weight as a side effect b) 61 or fewer patients will gain weight as a side effect c) 63 or more patients will gain weight as a side effect d) Between 61 and 68, inclusive, will gain weight as a side effect y 5.

• 1492677230-Homework Set 7-13.docx

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