calculus review exam #4 questions with
and answers
Rational Function
lim(x➡️a, (f(x)/g(x))) - ANSWER-= (0/0) or (inf/inf)
Apply L'Hôpital's Rule
lim(x➡️a, (f'(x)/g'(x)))
Indeterminate Difference
lim(x➡️a, (f(x)-g(x)) - ANSWER-=(inf-inf)
Apply L'Hôpital's Rule
lim(x➡️a, (f'(x)-g'(x))
Indeterminate Powers
lim(x➡️a, (f(x))^g(x))) - ANSWER-= 0^0 or inf^0 or 1^inf
Apply L'Hôpital's Rule
lim(x➡️a, ((f(x)/g(x))')
Curve Sketching
Essential Information - ANSWER-first derivative
second derivative
domain
asymptotes
holes
end behavior
symmetry
periodicity
extrema
inflection points
strategic points
INTG(x^p dx) - ANSWER-((x^(p+1))/(p+1)) + C
INTG(n dx) - ANSWER-nx + C
INTG(e^x dx) - ANSWER-e^x + C
True or False:
f(x)= (1/3)x^3 - x^2 - 3x +1 has two critical numbers - ANSWER-False
x= -1
Find the number of critical numbers for f(x)= (cosx)^2- sinx on [0, 2pi] - ANSWER-4
critical numbers:
and answers
Rational Function
lim(x➡️a, (f(x)/g(x))) - ANSWER-= (0/0) or (inf/inf)
Apply L'Hôpital's Rule
lim(x➡️a, (f'(x)/g'(x)))
Indeterminate Difference
lim(x➡️a, (f(x)-g(x)) - ANSWER-=(inf-inf)
Apply L'Hôpital's Rule
lim(x➡️a, (f'(x)-g'(x))
Indeterminate Powers
lim(x➡️a, (f(x))^g(x))) - ANSWER-= 0^0 or inf^0 or 1^inf
Apply L'Hôpital's Rule
lim(x➡️a, ((f(x)/g(x))')
Curve Sketching
Essential Information - ANSWER-first derivative
second derivative
domain
asymptotes
holes
end behavior
symmetry
periodicity
extrema
inflection points
strategic points
INTG(x^p dx) - ANSWER-((x^(p+1))/(p+1)) + C
INTG(n dx) - ANSWER-nx + C
INTG(e^x dx) - ANSWER-e^x + C
True or False:
f(x)= (1/3)x^3 - x^2 - 3x +1 has two critical numbers - ANSWER-False
x= -1
Find the number of critical numbers for f(x)= (cosx)^2- sinx on [0, 2pi] - ANSWER-4
critical numbers:
