MATH 126 EXAM 1 || A+ CERTIFIED.
determinate form correct answers always represent the same limit
indeterminate form correct answers represent limits which may or may not exist & may be equal
to any value
* 0/0
* inf/inf
* inf - inf
* 0 x inf
* 1^inf
* 0^inf
* inf^0
discretize correct answers take continuous interval & divide it into sub-intervals
quotient rule correct answers (lo d hi - hi d lo)/(lo^2)
d/dx sin(x) correct answers cos(x)
d/dx cos (x) correct answers -sin(x)
d/dx tan(x) correct answers sec^2(x)
d/dx csc(x) correct answers -csc(x)cot(x)
d/dx sec(x) correct answers sec(x)tan(x)
, d/dx cot(x) correct answers -csc^2(x)
product rule correct answers d/dx[f(x)g(x) = f'(x)g(x) + f(x)g'(x)
chain rule correct answers d/dx[f(g(x))] = f'(g(x))g'(x)
power rule correct answers d/dx[x^n] = nx^(n-1)
d/dx e^x correct answers e^x
d/dx a^x correct answers a^x ln(a)
d/dx log_a(x) correct answers 1/(x ln(a))
d/dx ln(x) correct answers 1/x
d/dx arcsin(x) correct answers 1/(sqrt(1-x^2))
d/dx arccos(x) correct answers -1/(sqrt(1-x^2))
d/dx arctan(x) correct answers 1/(1+x^2)
d/dx arccot(x) correct answers -1/(1+x^2)
d/dx arcsec(x) correct answers 1/(abs(x)sqrt(x^2+1))
d/dx arccsc(x) correct answers -1/(abs(x)sqrt(x^2+1))
determinate form correct answers always represent the same limit
indeterminate form correct answers represent limits which may or may not exist & may be equal
to any value
* 0/0
* inf/inf
* inf - inf
* 0 x inf
* 1^inf
* 0^inf
* inf^0
discretize correct answers take continuous interval & divide it into sub-intervals
quotient rule correct answers (lo d hi - hi d lo)/(lo^2)
d/dx sin(x) correct answers cos(x)
d/dx cos (x) correct answers -sin(x)
d/dx tan(x) correct answers sec^2(x)
d/dx csc(x) correct answers -csc(x)cot(x)
d/dx sec(x) correct answers sec(x)tan(x)
, d/dx cot(x) correct answers -csc^2(x)
product rule correct answers d/dx[f(x)g(x) = f'(x)g(x) + f(x)g'(x)
chain rule correct answers d/dx[f(g(x))] = f'(g(x))g'(x)
power rule correct answers d/dx[x^n] = nx^(n-1)
d/dx e^x correct answers e^x
d/dx a^x correct answers a^x ln(a)
d/dx log_a(x) correct answers 1/(x ln(a))
d/dx ln(x) correct answers 1/x
d/dx arcsin(x) correct answers 1/(sqrt(1-x^2))
d/dx arccos(x) correct answers -1/(sqrt(1-x^2))
d/dx arctan(x) correct answers 1/(1+x^2)
d/dx arccot(x) correct answers -1/(1+x^2)
d/dx arcsec(x) correct answers 1/(abs(x)sqrt(x^2+1))
d/dx arccsc(x) correct answers -1/(abs(x)sqrt(x^2+1))
