Enter each answer as a whole number or a fraction, or DNE for Does Not Exist or undefined.

Question

_x→1⁺  

_x→2^-    

_h→0   

Answer 1

This problem seems to be missing some information, such as what is f(x)?

Let's say f(x)=x

then the first limit as x approaches 1 is (1-2)/4 = - 1/2

and the 2nd limit as x approaches 2 is 2+2 = 4

the third limit is undefined 0/0. This last limit is part of how you can find the first derivative of a function, if you do it correctly, you get h in the denominator cancelling with an h in the numerator For example, take f(x)=x^2 and find the limit as x approaches 2. You're at the point (2,4) and want the slope of the tangent line at that point. You take f(x+h)-f(x) for the numerator, which is (x+h)^2-x^2 = x^2 +2hx + h^2 -x^2 = 2hx+h^2. The denominator is h which cancels giving (2hx+h^2)/h = 2x + h. Then let h go to zero to get 2x, which is the slope of the curve x^2 at the point (2,4), the first derivative

That suggests maybe this 3rd limit was copied wrong and was really find the limit as h approaches zero of (3.5+h)^2 - (3.5)^2 all over h. then you get

3.5^2 + 7h + h^2 - 3.5^2 or (7h+h^2)/ h = 7+ h. Let h go to zero and you get 7 as the limit

Answer 2

Kyle

You need to define f(x) here !

Mike