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Answers
Step-by-step explanation:
Explanation:
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Answer:
(1) 5
(2) 5/3
(3) 3/5
(4) 25
Step-by-step explanation:
(1) lim x→0 sin5x/x
using sinx/x = 1 and other tools
multiplying sin5x/x by 5/5
lim x→0 5sin5x/5x
taking, 5 on the side left of limit
5lim x→0 sin5x/5x
now here, 5x→0
5lim x→0 sin5x/5x
= 5(1) = 5
(2) lim x→0 tan5x/sin3x
using L′ Hospitals rule
= lim x→0 5sec²x/3cosx
= 5/3 lim x→0 sec²x/cosx
= 5/3 lim x→0 1/cos³x
put the limit 0 in 1/cos³x
=5/3(1) ... cos0° = 1
= 5/3
(3) lim x→0 sin3x/5x
using sinx/x =1
= lim x→0 sin3x/5x
= lim x→0 (sin3x/3x) × (3x/5x)
= 3/5
(4) lim x→0 sin²5x/x²
using sinx/x
= lim x→0 (sin5x)(sin5x)/(x)(x)
= lim x→ 0 [sin5x/x] × [sin5x/x]
= lim x→0 [5sin5x/5x] × [5sin5x/5x]
= 5× 5 =25