Question

I have a few problems from my homework that I am having trouble with.

#1 Find the difference quotient of f foreach function

f(x)=1/(x+3)

I got -2x+6

#2 Express the area of an isosceles right triangle as a function of the length x of one of the two eual sides


Thanks

Answer 1

The difference quotient,

∆f/∆x = [f(x+h)-f(x)]/h
= [1/((x+h)+3) - 1/(x+3)]/h
= 1/h [(x+3) - (x+h+3)] / (x+h+3)(x+3)
= 1/h (-h)/(x+h+3)(x+3)
= -1/[(x+h+3)(x+3)]


The legs are x and x. One leg is the base, the other leg is the height, so the area is 1/2 bh = 1/2 x^2

Why can't the hypotenuse be one of the equal sides? Because the hypotenuse is longer than either leg.

Answer 2

for the second problem what is th height??

Answer 3

ohh wait ok that was me just having a dumb moment haha. THANKS sooo much:)