- #1
physics604
- 92
- 2
1. lim θ→0 [itex]\frac{sinθ}{θ+tanθ}[/itex]
lim x→0 [itex]\frac{sinx}{x}[/itex]=1
lim x→0 [itex]\frac{cosx-1}{x}[/itex]=0
lim θ→0 [itex]\frac{sinθ}{θ+sinθ/cosθ}[/itex]
lim θ→0 [itex]\frac{sinθ}{(θcosθ+sinθ)/cosθ}[/itex]
lim θ→0 sinθ × [itex]\frac{cosθ}{θcosθ+sinθ}[/itex]
lim θ→0 [itex]\frac{θcosθ}{θcosθ+sinθ}[/itex]
The answer is supposed to be [itex]\frac{1}{2}[/itex]. What did I do wrong?
Homework Equations
lim x→0 [itex]\frac{sinx}{x}[/itex]=1
lim x→0 [itex]\frac{cosx-1}{x}[/itex]=0
The Attempt at a Solution
lim θ→0 [itex]\frac{sinθ}{θ+sinθ/cosθ}[/itex]
lim θ→0 [itex]\frac{sinθ}{(θcosθ+sinθ)/cosθ}[/itex]
lim θ→0 sinθ × [itex]\frac{cosθ}{θcosθ+sinθ}[/itex]
lim θ→0 [itex]\frac{θcosθ}{θcosθ+sinθ}[/itex]
The answer is supposed to be [itex]\frac{1}{2}[/itex]. What did I do wrong?