Posted by John on Sunday, September 26, 2010 at 8:22pm.
How would you find the limit of (secx-1)/(x^2) as x goes to 0 algebraically?
- Calculus - bobpursley, Sunday, September 26, 2010 at 8:41pm
change secx -1 to 1/cosx -1 to (1-cosx)/cosx
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)
- Calculus - MathMate, Sunday, September 26, 2010 at 8:48pm
Multiply top and bottom by (sec(x)+1) to get
Lim x->0 (sin(x)/x)=1
Lim x->0 cos(x)=1
Lim x->0 sec(x)=1
Lim x->0 (secx-1)/(x^2) = 1/2
Alternatively, use l'Hôpital's rule.
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