problem 1: The eighth term of an arithmetic progression is twice the fourth term. The seventh term is 14. Find the sum of 100 terms.
problem 2: The fourth term of a geometric progression is 4, and the seventh term is 0.5. Find the sum to infinity for this geometric progression.
problem 3: A geometric progression has the first term 10 and common ratio 1.5. The sum to n terms is 131.875. Find the value of n.
problem 4:
a) Differentiate the following functions:
f(x) = 1/x
g(x) = √(x^{2})^{3}
b) Differentiate the following functions:
f(z) = z^{3} (z^{-3/4} + z^{3/4} + z)
g(z) = 4/z^{3} – z^{3/4}
problem 5: Differentiate the following functions with respect to x:
a) f(x) = (x^{2} + 2x) exp(x)
b) g(x) = 1/(x^{2} – 1)
c) h(x) = exp(x(x+1))
d) j(x) = ln(1 + x + x^{2})
e) k(x) = e^{x}/(e^{x} – e^{-x})
problem 6: You are given the function f(x) = x^{2} - 3x + 2.
a) Find the equations of the tangents at the points where the function crosses the x-axis.
b) Find the point where the two tangents intersect.