calculus

posted by .

The limit represents the derivative of some function f at some number a. Select an appropriate f(x) and a.
lim (cos(pi+h)+1)/h
h->0

f(x) = tan(x), a = pi
f(x) = cos(x), a = pi/4
f(x) = cos(x), a = pi
f(x) = sin(x), a = pi

• calculus -

Using La'Hopital's rule...

lim = d/dx numerator/d/dx denominator

= -sin(pi+h)(1)/1= -sinPI
So none of the answers are really right, however, one can note that sinPI=-sinPI=0, so the last answer is right because it is zero. However, one could have written just as well
f(x)= 40.3 sinPI and that would be right. And because of this, equalling zero, the first answer is just as right. The question is not well crafted, unless I missed something.

Similar Questions

1. CALCULUS - need help!

Determine the limit of the trigonometric function (if it exists). 1. lim sin x / 5x (x -> 0) 2. lim tan^2x / x (x ->0) 3. lim cos x tan x / x (x -> 0)
2. Calculus

The limit below represents the derivative of some function f at some number a. State such an f and a. lim x-->2 2^x-4/x-2 f(x)=_______ a=_______
3. calculus

This limit represents the derivative of some function f at some number a. Select an appropriate f and a. 1f(x) = x4, a = 4 f(x) = x1/4, a = 4 f(x) = x1/4, a = 256 f(x) = ãx, a = 256 f(x) = ãx, a = 16
4. calc plzzzz help

This limit represents the derivative of some function f at some number a. Select an appropriate f and a. lim_(h->0) (root4(256+h)-4)/h 1 f(x) = x^4, a = 4 f(x) = x^1/4, a = 4 f(x) = x^1/4, a = 256 f(x) = √x, a = 256 f(x) = …
5. calculus

The limit represents the derivative of some function f at some number a. Select an appropriate f(t) and a. lim_(t->1)(t^3+t-2)/(t-1) 1f(t) = t^3, a = 1 f(t) = t^3 + t, a = 1 f(t) = t - 2, a = 1 f(t) = t - 2, a = -1 f(t) = t^3 + …
6. calculus

The limit lim as x approaches 1 of (x^12-1)/(x-1) represents the derivative of some function f(x) at some number a. Find f and a.
7. calculus

The limit as x approaches 0 of ((4^x)-1)/x The limit above represents the derivative of some function f(x) at some number a. Find f and a.
8. calculus

the limit represents the derivative of some function f at some number a. state f and a. lim (sin(pai/2 + t)-1)/t t->0
9. Calculus I

We're reviewing limits from the previous chapter, but I'm still having some difficulty with some problems: lim tan(pi(x/4)) as x-> -7 lim (x^2 - x^3(cos(1/x))/3x^2 as x-> 0 I know the answer to the first problem is 1 and to the …

The limit limh->0 ((sqrt1+h)-1)/h represents the derivative of some function f(x) at some number a. Find f and a. Please help!

More Similar Questions