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Math
Calculus
Pre-Calculus TEST 2
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Gravity
Terms in this set (20)
x<0 means
negative
x>0 means
positive
in rational inequalities
VA's=rounded parentheses
X-intercepts=Brackets
to get an x intercept of an inequality...
equal the numerator to 0
to get the VA of an inequality...
equal the denominator to 0
To find the inverse of a function
1 switch x and y
2 equal to f^-1(x)
3 verify by plugging in f(x) into f^-1(x) your supposed to get X by itself.
exponential functions special points are...
(-1,1/a) (0,1) (1,a)
when a sign is outside of parentheses...
you follow the sign up or down
when the sign is on the leading terms exponent you...
reflect across the y axis
type in 2nd then hit LN on your calculator to get...
the value of E
when switching from logarithm and exponential...
switch the y an x value and add a log before the base.
y=a^x to x=log a^y
logarithms can't be...
negative or they are not real
less than the base and exponent or they are 0.
exponential functions...
d=(-👀,👀)
r=(0,👀)
logarithmic is the opposite
common and natural...
log10x=log x
loge^x=LnX
if the sign is in the parentheses...
shift horizontally left or right but do the opposite of what the sign is.
product rule...
logbM+logbN = logb(M*N)
quotient rule...
logb(M/N) = logbM-logbN
power rule...
logbM^r = RlogbM
when bases...
when bases match= 1
when result is 1= 0
to find the sum or difference of logarithms
1 start with quotient rule /
2 continue with product rule x
3 continue with power rule exp
4 look at the base properties such as LNe=1; log1=0; log10=1
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Verified questions
QUESTION
Use the guidelines of Section 4.5 to sketch the curve. $$ y=x/1-x^2 $$
CALCULUS
Solve the initial-value problem. $$ dr/dt+2tr=r, r(0)=5 $$
CALCULUS
After running 3 miles at a speed of x mph, a man walked the next 6 miles at a speed that was 2 mph slower. Express the total time spent on the trip as a function of x. What horizontal and vertical asymptotes does the graph of this function have?
CALCULUS
Evaluate $$ ^1∫0(x+√1-x^2)dx $$ by interpreting it in terms of areas.