Week 4

Question 1

Derivative of inverse?

Answer 1

reciprocal of normal function derivative

Question 2

arctanx?

Answer 2

1/tanx

Question 3

Primitive?

Answer 3

integral of a derivative

indefinite integral if there are many functions we can differentiate to get the integral

e.g. e^x and e^x +5

Question 4

Fundamental theorem of calculus?

Answer 4

G(x) = upper limit x ∫ f(t)

G’(x) = f(x)

​

Question 5

∫ 1/x^+1 ?

Answer 5

arctan(x) + c

Question 6

∫ 1/√1-x^2 ?

Answer 6

arcsin(x) +c

Question 7

How to calculate improper integrals?

Answer 7

-use m and as m tends to infinity (if limits are infinity)

-use m and as m tends to limit (if f(x) is too big from that point)

m+ if approaching from RHS and m- if approaching from LHS

Question 8

Fraction when denominator tends to 0?

Answer 8

infinity

Question 9

Ln (1/e)

Answer 9

-1

Question 10

Derivative of a^x

Answer 10

a ln a

Question 11

Derivative of a^u , where a is a constant and u is a function?

Answer 11

a^u ln (a) du/dx

Question 12

Derivative of e^u , where u is a function?

Answer 12

du/dx e^u