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Evaluate following limits.
Solution
In this case we also contain a 0/0 indeterminate form and if we were actually good at factoring we could factor the numerator & denominator, simplify and take the limit. Though, that's going to be more work than just utilizing L'Hospital's Rule.
L'Hospital's Rule works greatly on the two indeterminate forms 0/0 and ± ∞ /± ∞ . Though, there are several more indeterminate forms out there as we illustrated earlier. Let's see some of those and see how we can deal with those types of indeterminate forms.
We'll begin with the indeterminate form (0) ( ± ∞ ) .
A sphere and a cube have equal surface areas. Show that the ratio of the volume of the sphere to that of the cube is √6 : √π. Ans: S.A. of sphere = S.A of cube 4π r 2
sin10+sin20+sin30+....+sin360=0 sin10+sin20+sin30+sin40+...sin180+sin(360-170)+......+sin(360-40)+sin(360-30)+sin(360-20)+sin360-10)+sin360 sin360-x=-sinx hence all terms cancel
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