PASS Calculus Jeoprady

L'hospital's Rule

100

When do we use L'hospital's rule to solve limits?

When direct substitution gives 0/0 or ∞ /∞ 

200

ℓimx↦0(-sinx/2x)

-1/2

300

ℓimx↦π(tan(2x)/(x-π))

2

400

ℓimx↦π((1+cosx)/sin2x)

0

500

ℓimx↦0 ((2cosx-2+x²)/3x⁴)

1/36

Inverse trig derivatives

100

what is the derivative of arcsin(x)?

1/√(1-x²)

200

What is the derivative of arctan(□ )?

1/√(1+□ ²) · □'

300

limx→0 Arcsin(x)/Arctan(x)

1

400

d/dx (sin (2Arcsinx) ) , at x=0

2

500

what is the derivative of Arccsc(x)?

-1/(|x|√x²-1)

Properties of log

100

T or F : log_a(Δ□)   = Δ log_a(□)

False (log_a(□)^Δ   = Δ log_a(□))

200

Simplify log₄ (2^x16^-x2)

(x/2) - 2x

300

d/dx log₄(2x+1) ,  at x=0

2/ln4

400

differentiate: log₂(√ x+1)

1/ (2ln2(x+1))

500

differentiate: log4(x³+x+1)

(3x²+1)/ln4(x³+x+1)

Properties of Natural log

100

T or F : e^ln(2x+3) = 1

False (=2x+3)

200

ln(e) = ?

1

300

4ln(x+2)

4/(x+2)

400

ln(x³+3) at x=1

3/4

500

differentiate: e^x/logx

e^x(xlogx-1)/x(logx)²