Download 34 Problems on Brief Calculus - Final Exam | MAT 210 and more Exams Mathematics in PDF only on Docsity!
Naala Brewer Brewer MAT 210 Fall 2008
WeBWorK assignment number Final Exam Review is due : 12/01/2008 at 07:34pm MST. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor for help. Don’t spend a lot of time guessing – it’s not very efficient or effective. Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 ∧ 3 instead of 8, sin( 3 ∗ pi/ 2 ) instead of -1, e ∧ (ln( 2 )) instead of 2, ( 2 + tan( 3 )) ∗ ( 4 − sin( 5 )) ∧ 6 − 7 /8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands. You can use the E-mail instructor button on each problem page to send e-mail to the professors.
1. (1 pt) Evaluate the limit lim x → 3
( 8 x^2 + 5 )( 6 x + 5 )
If the limit does not exist enter DNE. Limit = Correct Answers:
- 1771 2. (1 pt) Evaluate the limit
lim x →− 10
x^2 + 17 x + 70 x + 10
If the limit does not exist enter DNE. Limit = Correct Answers:
3. (1 pt) Evaluate the limit
lim x →− 8
x^2 − 64 x + 8
If the limit does not exist enter DNE. Limit = Correct Answers:
4. (1 pt) Evaluate the limit
lim x → 1
x^2 + 2 x − 3 x − 1
If the limit does not exist enter DNE.
Correct Answers:
lim x →∞
3 − 7 x^4 5 + 4 x^4
If the limit is ∞, enter ’INF’, and if the limit is −∞, then enter ’-INF’. Limit = Correct Answers:
lim x →∞
5 x^4 + 6 10 x^2 + 3
If the limit is ∞, enter ’INF’, and if the limit is −∞, then enter ’-INF’. Limit = Correct Answers:
- INF 7. (1 pt) Evaluate the limit
lim x →∞
10 x^3 − 10 x^2 − 3 x 11 − 11 x − 9 x^3 If the limit does not exist enter DNE. Limit = Correct Answers:
f ( x ) =
1 + x , x < 2 , 5 − x , x ≥ 2.
Find the indicated one-sided limits of f , and determine the continuity of f at the indicated point. NOTE: Type DNE if a limit does not exist. You should also sketch a graph of y = f ( x ), including hollow and solid circles in the appropriate places. lim x → 2 −^
f ( x ) = lim x → 2 +^
f ( x ) = lim x → 2 f ( x ) = f ( 2 ) = Is f continuous at x = 2? (YES/NO) Correct Answers:
9. (1 pt) Let
f ( x ) =
− 7 x , x < 2 , 1 , x = 2 , 7 x , x > 2. Find the indicated one-sided limits of f , and determine the continuity of f at the indicated point. NOTE: Type DNE if a limit does not exist. You should also sketch a graph of y = f ( x ), including hollow and solid circles in the appropriate places. lim x → 2 −^
f ( x ) = lim x → 2 +^
f ( x ) =
lim x → 2 f ( x ) = f ( 2 ) = Is f continuous at x = 2? (YES/NO) Correct Answers:
- 14
- DNE
- 1
- NO 10. (1 pt) Evaluate
d dx
e^4 x
(^2) + 3 x . d dx
e^4 x (^2) + 3 x = Correct Answers:
- (8x+3)exp(4xˆ2+3x) 11. (1 pt) Evaluate
d dt
(ln( t^2 + 6 ))^8. d dt
(ln( t^2 + 6 ))^8 = Correct Answers:
- 2t8*ln(tˆ2+6)ˆ7/(tˆ2+6) 12. (1 pt) Suppose that f ( x ) = ( 2 x − 4 )^2 ( 2 x^2 + 1 )^3.
Find f ′( x ), and then evaluate f ′^ at x = 1 and x = −1. f ′( 1 ) = f ′(− 1 ) = Correct Answers:
13. (1 pt) If f ( x ) =
3 x + 2 2 x + 3
find f ′( x ).
Find f ′( 1 ).
Correct Answers:
- 5/[(2*x+3)ˆ2]
14. (1 pt) Let f ( t ) = ( t^2 + 5 t + 7 )( 3 t^2 + 2 ). (a) f ′( t ) = (b) f ′( 5 ) = [NOTE: Your answer to part (a) should be a function in terms of the variable ’t’ and not a number! Your answer to part (b) should be a number.] Correct Answers:- (2t+5)(3tˆ2+2)+(tˆ2+5t+7)6t
- 2865 15. (1 pt) For the equation given below, evaluate y ′^ at the point (− 1 , 2 ).
2 y^3 + y^2 − 4 x^2 = 16.
y ′^ at (− 1 , 2 ) = Correct Answers:
- -0. 16. (1 pt) Find the absolute maximum and absolute minimum values of the function
f ( x ) = x^4 − 8 x^2 − 3
on each of the indicated intervals. Enter None for any absolute extrema that do not exist. (A) Interval = [− 3 , − 1 ]. Absolute maximum = Absolute minimum = (B) Interval = [− 4 , 1 ]. Absolute maximum = Absolute minimum = (C) Interval = [− 3 , 4 ]. Absolute maximum = Absolute minimum = Correct Answers:
21. (1 pt) Use linear approximation, i.e. the tangent line, to approximate 3
125 .04 as follows. Let f ( x ) = 3
x and find the equation of the tangent line to f ( x ) at x = 125 in the form y = mx + b. Note: The values of m and b are rational numbers which can be computed by hand. You need to enter expressions which give m and b exactly. You may not have a decimal point in the answers to either of these parts. m = b = Using these values, find the approximation. √ (^3125). 04 ≈
Note: You can enter decimals for the last part, but it will has to be entered to very high precision (correct for 6 places past the decimal point). Correct Answers:
- 1/(3*5ˆ2)
- 5 - 125/(3*5ˆ2)
22. Z (1 pt) Evaluate the indefinite integral: 6 x^2 + 3 x − 3 dx = + C. Correct Answers:
- 2xˆ3+1.5xˆ2-3*x 23. (1 pt) Evaluate the indefinite integral: Z 9 x^2 x^3 + 2
dx = + C. Correct Answers:
- 3*ln(|xˆ3+2|) 24. (1 pt) Evaluate the indefinite integral.Z x^5
11 + x^6 dx
Correct Answers:
- 0.111111*(xˆ6+11)ˆ1. 25. (1 pt) Evaluate the indefinite integral.Z x + 3 x^2 + 6 x
dx
- 0.5ln(|xˆ2+6x|) 26. Z (1 pt) Evaluate the indefinite integral: 4 xe^2 x
2 dx = + C. Correct Answers:
- 1exp(2xˆ2) 27. Z (1 pt) Evaluate the indefinite integral: e^9 x ( 2 + e^9 x )^3 dx = + C. Correct Answers:
- [2+exp(9*x)]ˆ4/ 28. Z (1 pt) Evaluate the definite integral: 3 0
( e^3 x^ − 3 x )^4 ( e^3 x^ − 1 ) dx = Correct Answers:
- 2.31604640790296E+ 29. (1 pt) Evaluate the indefinite integral: Z 3 − 6 x^4 x^2 dx = + C. Correct Answers:
- -3/x-6*xˆ3/ 30. (1 pt) Use integration by parts to evaluate the integral.Z xe^2 xdx
- 0.5[xeˆ(2x)-0.5eˆ(2*x)] 31. (1 pt) Use integration by parts to evaluate the definite integral. Z (^2)
0
te − t^ dt
Correct Answers:
- -2 * 2.71828182845905ˆ(-2) - 2.71828182845905ˆ(-2) + 1 32. (1 pt) A population of cattle is increasing at a rate of 200 + 40 t per year, where t is measured in years. By how much does the population increase between the 9 th and the 15 th years. Total Increase = Correct Answers:
- 4080 33. (1 pt) Determine whether the integral is divergent or con- vergent. If it is convergent, evaluate it. If not, state your answer as ”divergent.” (^) Z ∞ 0
2 e − xdx
Correct Answers:
- 2 34. (1 pt) Determine whether the integral is divergent or con- vergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as ”INF” (without the quotation marks). If it diverges to negative infinity, state your answer as ”MINF”. If it diverges without being infinity or negative infinity, state your answer as ”DIV”. (^) Z ∞
- 1
e −^1.^2 x^ dx
Correct Answers:
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