Monday

September 22, 2014

September 22, 2014

Posted by **John** on Sunday, September 26, 2010 at 8:22pm.

- Calculus -
**bobpursley**, Sunday, September 26, 2010 at 8:41pmchange secx -1 to 1/cosx -1 to (1-cosx)/cosx

then

lim (1-cosx)/(cosx)x^2 rationalize the numberator.

lim (1-cosx)(1+cosx)/(1+cosx)cosx x^2

lim (sin^2x)/x^2 * 1/(1+cosx)cosx

lim (sinx/x)lim sinx/x Lim (1/(cosx)(1+cosx)

1*1*1/(1*2)= 1/2

- Calculus -
**MathMate**, Sunday, September 26, 2010 at 8:48pmMultiply top and bottom by (sec(x)+1) to get

(secx-1)(sec(x)+1)/((x^2)(sec(x)+1)

=(sec²(x)-1)/((x^2)(sec(x)+1)

=(sin(x)/x)²/(cos²(x)(1+sec(x)))

Lim x->0 (sin(x)/x)=1

Lim x->0 cos(x)=1

Lim x->0 sec(x)=1

Therefore

Lim x->0 (secx-1)/(x^2) = 1/2

Alternatively, use l'Hôpital's rule.

**Answer this Question**

**Related Questions**

calculus - (a) Find the number c such that the limit below exists. Limit as x ...

Calculus - Show that the limit for [x^2cos(1/x)]=0 as x approaches 0. How would ...

Calculus - I am sorry. I am really struggling with limits. I am not sure of an ...

calculus - find the lim x->0 (e^(-x) -1) / (1-e^x) i did this using a table ...

Calculus Please Help - Hello I'm reposting this question because right now it's ...

Calculus - Find the indicated one sided limits of f. f(x)= (x^2+8)/(x^2-25) what...

Calculus - Limit as x approaches (pi/2)^- of (x-pi/2)*secx

Calculus - find the derivative y= csc^-1 (secx) 0 less than or equal to x less ...

Math - (a) Find the number c such that the limit below exists. Limit as x goes ...

calculus ap - find limit as x goes to infiniti of 8x^4-3x^2+2 over 9x^5+7x^4-3x^...