PCHA final exam/25 Questions and Answers A+ Graded

PCHA final exam/25 Questions and
Answers A+ Graded
limit definition - -f(x+h) - f(x) / h

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

-derivative of tan(x) - -sec2(x)

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

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

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

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

-derivative of ln(a) - -1/a * (da/dx)

-derivative of log a (u) - -1/(u * ln(a) * (du/dx)

-recursive arithmetic sequence - -a(n+1) = a(n) + d

-explicit arithmetic sequence - -a(n) = a(1) + d(n-1)

-recursive geometric sequence - -a(n+1) = a(n)*r

-explicit geometric sequence - -a(n) = a(1) * r^(n-1)

-arithmetic summation notation - -n
∑ a(k) = S(n)
k=1

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

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

if |r| < 1 (converges)