Question

Evaluate the trigonometric limit.

lim
x→0 sin(πx)^2/7x^2

Answer 1

\[\lim_{x \rightarrow 0} \sin^2(\pi x)/7x^2 \]

Answer 2

please do not use l'hopital

Answer 3

Use L'Hopital's Rule.

Answer 4

Ah, why not?

Answer 5

can't we haven't learned that

Answer 6

that is not how the teacher wants it solved

Answer 7

What lesson are you learning? It seems to me that L'Hopital is the only way to solve this.

Answer 8

one second

Answer 9

One second?

Answer 10

looking at my notes

Answer 11

we have been learning implicits but i don't see how it applies

Answer 12

and just general trig differentiation

Answer 13

Trig identies could be used.

Answer 14

Then multiply by conjugate.

Answer 15

Should work out smoothly...

Answer 16

@Dido525 What about denominator?

Answer 17

Hmm let me try...

Answer 18

For very small angles sin y = y
\[\lim_{x \rightarrow 0}\sin (\pi x)^{2}=(\pi x)^{2}\]
\[\lim_{x \rightarrow 0}\frac{(\pi x)^{2}}{7x ^{2}}=?\]

Answer 19

\[\frac{(\pi x)^{2}}{7x ^{2}}=\frac{\ \pi ^{2}}{7}\]

Answer 20

i plugged in wolfram and it said\[ \pi^2/7 \]