PCHA Final Exam Questions & Answers 100% Correct!!

PCHA Final Exam Questions & Answers
100% Correct!!
limit definition - ANSWERSf(x+h) - f(x) / h

parametric equations for ferris wheel - ANSWERSx(t) = a * sin(t)
y(t) = a * -cos(t) + k

derivative of tan(x) - ANSWERSsec2(x)

derivative of cot(x) - ANSWERS-csc2(x)

derivative of sec(x) - ANSWERSsec(x)tan(x)

derivative of csc(x) - ANSWERS-csc(x)cot(x)

derivative of a^x - ANSWERS(a^x)*ln(a)*(da/dx)

derivative of ln(a) - ANSWERS1/a * (da/dx)


Second derivative test - ANSWERSf has a relative maximum value at c if f'(c) < 0 and a
relative minimum value at c if f'(c) > 0. If f'(c) = 0, the test is not informative.

Things to remember: - ANSWERS"+c" for anti-derivatives

numbers have to add up for hypergeometric problems

always write limit sign in front of equation when solving

plug numbers back in when working with parametric equations arithmetic summation
notation - ANSWERSn
∑ a(k) = S(n)
k=1

geometric summation notation - ANSWERSn (= number in sequence)
∑ a(n) = a(1) * ( 1 - r^n ) / (1-r)
n=1

infinite summation notation - ANSWERS∞
∑ a(k) = a(1) / (1-r)
k=1