# Defenition of Limit

#### Tails

Joined Feb 13, 2007
5
I'm stuck on a calc problem, and its lim of tanx.

Here is the whole thing:

By using the defenition f'(a)=lim (f(a+h)-f(a))/h and taking smaller

values of h, estimate the value of f'(pi/4).

When i plug in the limit definition, the numbers really seem to jump around, or is that what i use to find the values? Anyway, can somebody help me with this problem? its due tomorrow. Thanks.

NOTE: due to the lack of symbols, "pi" is used in place of the greek letter

#### Papabravo

Joined Feb 24, 2006
16,794
I'm stuck on a calc problem, and its lim of tanx.

Here is the whole thing:

By using the defenition f'(a)=lim (f(a+h)-f(a))/h and taking smaller

values of h, estimate the value of f'(pi/4).

When i plug in the limit definition, the numbers really seem to jump around, or is that what i use to find the values? Anyway, can somebody help me with this problem? its due tomorrow. Thanks.

NOTE: due to the lack of symbols, "pi" is used in place of the greek letter
Then you are doing something wrong. The limit you are taking is an approximation to the derivative of tan(x), not the value of the function itself. The answers that you get should be closer and closer to 2, which is the value of the derivative of tan(x) at pi/4. Is your calculator set for degrees or radians? To compute tan(pi/4) you need to make sure that it is set to radians.
Rich (BB code):
((tan(pi/4 + .01) - tan(pi/4)))/.01 = 2.02...
((tan(pi/4 + .001) - tan(pi/4)))/.001 = 2.002...
d(tan(x))/dx = 1 / cos^2(x) = 1 /(.707)^2 = 1 / 0.5 = 2

you can also make h negative and approach the value from the other side.

#### Tails

Joined Feb 13, 2007
5
i was doing it wrong... i was looking at "h" as being "a" (pi/4) and i realized "h" shouldve been 0 in the table, and i looked, and the answers do approach 2 when the x value in my calc is 0, which is h.

#### Papabravo

Joined Feb 24, 2006
16,794