# Calculus

posted by .

evaluate the limit:

lim cos(x + pi/2)/x
x->0

• Calculus -

cos(x+pi/2)
= cosx cos pi/2 - sinx sin pi/2
= 0 - sinx
= -sinx

so
limit cos(x+pi/2)/x as x----> o
= lim -sinx/x , x ---> 0
= -1

using the fact that lim sinx/x = 1

## Similar Questions

1. ### Calculus

yes! tnk u ok? It's actually (x->0.) Find the limit of cot(x)-csc(x) as x approached 0?
2. ### 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)
3. ### calculus

calculate the lim as x-> pi (cos(x)+1)/(x-pi) using the special limit lim x->0 sinx/x
4. ### math

i need some serious help with limits in pre-calc. here are a few questions that i really do not understand. 1. Evaluate: lim (3x^3-2x^2+5) x--> -1 2. Evaluate: lim [ln(4x+1) x-->2 3. Evaluate: lim[cos(pi x/3)] x-->2 4. Evaluate: …
5. ### Calculus

Evaluate each limit. If it exists. a) Lim x^3 + 1 x->1 ------- x + 1 b) Lim 3x^2 - x^3 x->0 ---------- x^3 + 4x^2 c) Lim 16 - x x->16 --------- (√x) - 4

4. lim (tanx)= x->pi/3 -(sqrt3) 1 (sqrt3) ***-1 The limit does not exist. 5. lim |x|= x->-2 -2 ***2 0 -1 The limit does not exist. 6. lim [[x]]= x->9/2 (Remember that [[x]] represents the greatest integer function of x.) 4 …