Question

Find ModifyingBelow lim With h right arrow 0limh→0StartFraction f (x plus h )minus f (x )Over h EndFraction f(x+h)−f(x) h for the given function and value of x. ​f(x)equals=88xminus−77​, xequals=3

Answer 1

Answer:

Answer is 88

Step-by-step explanation:

We have Given function

$f(x)=88x-77$

we have to find f'(x) at x=3  Where f'(x) shows derivative of the given function.

This means we need

f'(3)=?

So By definition of the Derivative that is

$f'(x)=lim(h---->0)(f(x+h)-f(x))/h$

so this our definition of derivative of the function

Now We have to find out at x=3, So By putting x =3 in definition ,We get

f'(3)=lim(h---->0)(f(3+h)-f(3))/h

   Here lim(h--->0) means limit h approaches to zero(right arrow 0limh→0)

     =lim(h---->0)((88(3+h)-77))-(88(3)-77))/h

     =lim(h---->0)((264+88h-77)-264+77)/h

     =lim(h----->0)(264+88h-77-264+77)/h

now by performing simple arithematic we get result

f'(3) = lim(h---->0)(88h/h)

f('3) = lim(h---->0)(88)

here we use law of the limit we limit of the constant is that constant

lim(h----->0)c=c

so

f'(3)=88

So this our answer