2 Calculus 1 questions! Help please!

Q#1: Find the average rate of change of the function over the given interval --> h(t)=cot t [pi/4 ,3pi/4]
Q#2: Find the limit of the function [(1/x)-1] / x-1 as x approaches 1.

These are the only homework problems that I didn't get so full explanations are much appreciated. Thanks.

Question one says find the slope of the secant line on the interval:

cot(pi/4) = 1, cot(3pi/4) = -1

(-1 - 1) / (3pi/4 - pi/4) = -2 / pi/2 = -4 / pi
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Q#2: Find the limit of the function [(1/x)-1] / (x-1) as x approaches 1

This is a disguised derivative problem.

Recall that the definition of derivative is:

Limit as x goes to a of: [f(x) - f(a)] / [x - a]

If f(x) = 1/x then your question is what is the value of the derivative of 1/x at x = 1

f '(x) = -1/x^2, f '(1) = -1/(1)^2 = -1

OR

Algebraically simplify the expression [(1/x)-1] / (x-1) by multiplying numerator and denominator by x:

[(1/x)-1] * x / [(x-1) * x] = (1 - x) / [(x - 1) * x] = -1/x

limit as x-->1 (-1/x) = -1

lim x->1 (1/x - 1)/(x - 1)

Algebraic solution:

lim x->1 (1 - x)/x(x - 1) = lim x->1 -(x - 1)/x(x - 1) = lim x->1 -1/x = -1