Solving this trig limit without L'hopital: lim x → 1 sin ⁡ ( π x...

Carly Cannon

Carly Cannon

Answered

2022-07-08

Solving this trig limit without L'hopital: lim x 1 sin ( π x ) x 1
One idea I had was to multiply both sides of the fractions by
π x
like this
lim x 1 sin ( π x ) π x π x 2 π x
to cancel out the sine but then I realized that I could not do that because x tends to 1, and not to 0. What can I do?

Answer & Explanation

Madden Luna

Madden Luna

Expert

2022-07-09Added 9 answers

lim h 0 sin ( π ( 1 h ) ) 1 1 h
(Multiply and divide by pi) lim h 0 sin ( π h ) π π h
π
Sylvia Byrd

Sylvia Byrd

Expert

2022-07-10Added 6 answers

lim x 1 sin ( π x ) 1 x = lim h 0 sin ( π ( 1 h ) ) h = lim h 0 sin ( π h ) h (common limit) = lim h 0 sin ( π h ) π π h = π .

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