Calculus Study guides, Class notes & Summaries
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Business Calculus Test 1 Exam Questions with Correct Answers
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power rule - ANSWER-if y = x^k -- then, 
k * x^k⁻¹ 
 
product rule - ANSWER-f(x) • g(x) then 
[f(x)•g(x)' + f(x)'•g(x)] 
 
quotient rule - ANSWER-D(x) • N'(x) - N(x) •D'(x) 
--------------------- 
 [D(x)]² 
 
extended power rule - ANSWER-[g(x)]^k = 
k[g(x)]^k-1 • g(x)' 
 
chain rule - ANSWER-[f of g(x)]' = 
[f(g(x))]' = 
f'(g(x)) • g'(x) 
 
high order derivatives - ANSWER- 
 
what does a second derivative represent? - ANSWER-the rate of change of the rate of change 
...
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Calculus 1 exam 2 Exam Questions and Answers
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equation of a tangent line - ANSWER-y= f'(x)(x-x1)+f(x) 
 
difference quotient/ average rate of change (AROC) - ANSWER-f(x+h)-f(x)/h 
 
point slope form of a line - ANSWER-y-y1=m(x-x1) 
 
derivative is the same as... - ANSWER--slope of the tangent line 
-instantaneous rate of change 
-marginal (cost, profit, revenue) 
 
slope of the secant line - ANSWER-msec= (y2-y1)/(x2-x1) 
 
constant rule - ANSWER-if C is a real number, then the derivative of C =0 
 
power rule - ANSWER-if n is a nonnegative...
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Calculus 1 Exam 3 Prep Questions and Answers
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Points of Inflection - ANSWER-If (c, f(c)) is a point of inflection of the graph of f, then either f"(c)=0 or f" is undefined at c 
 
Critical Value - ANSWER-Where first derivative is 0 or undefined 
 
Find absolute extrema - ANSWER-Use critical values and END POINTS in the function 
 
Horizontal Asymptote Rules - ANSWER-If m>n: NO HA 
If m=n: HA = co-eff of m/co-eff of n 
If m<n: HA: y = 0 
 
Mean Value Theorem - ANSWER-if f(x) is continuous on [a,b] and differentiable on (a,b), there i...
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Calculus 1 Final exam review Questions with Latest Update
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definition of a limit - ANSWER-A limit is a number that a function approaches as x approaches a value 
 
Limit equation - ANSWER-f(x+h)-f(x)/h 
 
e ln(x) - ANSWER-x 
 
e^x e^y - ANSWER-e^(x+y) 
 
e^xy - ANSWER-(e^x)^y 
 
lne^x - ANSWER-x 
 
ln(xy) - ANSWER-ln(x)+ln(y) 
 
ln(x^y ) - ANSWER-ylnx 
 
tan theta - ANSWER-sin theta/cos theta 
 
secant of theta - ANSWER-1/cos theta 
 
cot theta - ANSWER-cos theta/sin theta 
 
csc theta - ANSWER-1/sin theta 
 
lim x->c (f(x) + g(x)) - ANSWER-lim x->...
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Calculus Exam 1 Questions with Latest Update
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What will calculus enable you to do? - ANSWER-Find the volumes of oddly shaped objects 
 
Consider the function y=x^2-2x+1. What is the slope of the tangent line at x=2? - ANSWER-2 
 
What is the average rate of change of the function y=2x^2+3 between x=x1 and x=x2 - ANSWER-2(x2+X1) 
 
What is the slope of the secant line of the function y=4x^2-2x+1 between x=3 and x=6 - ANSWER-34 
 
A body is thrown upward so that its height h at the end of t seconds is h=160t-16t^2. What is its max height? - A...
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Calculus Exam 2 Questions and Answers
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Power Rule - ANSWER-d/dx x^n = nx^n-1 
 
d/dx [c] - ANSWER-0 
 
d/dx [sinx] - ANSWER-cosx 
 
d/dx [cosx] - ANSWER--sinx 
 
d/dx [e^x] - ANSWER-e^x 
 
Product Rule - ANSWER-d/dx [f(x) g(x)] = f'g+g'f 
 
Quotient Rule - ANSWER-d/dx [f(x)/g(x)] = f'g-g'f/g^2 
 
d/dx [tanx] - ANSWER-sec^2x 
 
d/dx [secx] - ANSWER-secxtanx 
 
d/dx [cotx] - ANSWER--csc^2x 
 
d/dx [cscx] - ANSWER--cscxcotx 
 
Chain Rule - ANSWER-d/dx [f(g(x))] = f'(g(x)) * g'(x) 
 
Inside/Outside Properties - ANSWER-y=(inside)^n ...
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Calculus exam 3 Questions with Verified Answers
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volume equation - ANSWER-v=4/3 r^3 
 
related rate problems - ANSWER-treat all variables as functions of time, use implicit differentiation to produce equalities which can be solved for the desired rates 
 
linear approximation equation - ANSWER-f'(a)(x-a)+f(a) 
 
linear approximation - ANSWER-approximating functions using the equation of a line, also known as tangent line approxiamtion 
 
equation for dy - ANSWER-f'(x)dx or f'(x)delta x 
 
dy - ANSWER-differential, dependent on both the valu...
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Calculus Exam 4 Questions with Latest Update
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INTG(sin(x) dx) - ANSWER--cos(x) + C 
 
INTG(cos(x) dx) - ANSWER-sin(x) + C 
 
INTG((sec(x))^2 dx) - ANSWER-tan(x) + C 
 
INTG((csc(x))^2 dx) - ANSWER--cot(x) + C 
 
INTG(sec(x)*tan(x) dx) - ANSWER-sec(x) + C 
 
INTG(csc(x)*cot(x) dx) - ANSWER--csc(x) + C 
 
INTG(b^x dx) - ANSWER-(1/ln(b))*b^x + C 
 
INTG(1/x dx) - ANSWER-ln(abs(x)) + C 
 
INTG((1/sqrt(1-x^2)) dx) - ANSWER-arcsin(x) + C 
 
INTG(-(1/sqrt(1-x^2)) dx) - ANSWER-arccos(x) + C 
 
INTG((1/(1+x^2)) dx) - ANSWER-arctan(x) + C 
 
Rational...
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Calculus Exam One Practice Problems Questions and Answers
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∫ 2x / (x² - 1) - ANSWER-Method: U sub 
HW 6 #1 
Answer: ln(x+1) + ln(x-1) + C 
 
∫ x - 8 
x² + 2x - 8 - ANSWER-Method: Partial Fractions 
HW 6 #3 
Answer: 2 ln(x+4) - ln(x-2) + C 
 
∫ 9x - 25 
3x² - 13x + 4 - ANSWER-Method: Partial Fractions 
HW 6 #5 
Answer: 2 ln(3x-1) + ln(x-4) + C 
 
∫ x² + 4x + 5 
x³ + x² + x + 1 - ANSWER-Method: Partial Fractions 
HW 6 #7 
Answer: 4 tan⁻¹(x) + ln(x+1) + C 
 
∫ 4x² + 11 
x³ + x² + 4x + 4 - ANSWER-Method: Partial Fractions 
HW 6 #9 
An...
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Calculus Final Exam Questions with Correct Answers
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Vertical Asymptote - ANSWER-Set Denominator equal to zero 
 
Horizontal asymptote - ANSWER-set numerator equal to zero 
 
Rolles theorem states there is... - ANSWER-a tangent line at some point on a closed interval [a,b] if the following hold true 
a) continuous 
b) differentiable 
c) f(a)=f(b) 
 
Integration is a... - ANSWER-continuous addition process 
 
Intermediate Value Theorem: Suppose f is a function continuous at every point on the interval [a,b]: - ANSWER-a) f will take on every value b...
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