What is the limit as x approaches 0 of (sin(7x))/(tan(5x)) ?

The limit as x approaches 0 of (sin(7x))/(tan(5x)) is 7/5

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limit as x approaches 0 of (sin(7x))/(tan(5x))

x \to 0 lim (\frac{sin ( 7 x )}{tan ( 5 x )})

\frac{7}{5}

Decimal

1.4

Solution steps

x \to 0 lim (\frac{sin ( 7 x )}{tan ( 5 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 7 x ) \cdot 7}{sec ^{2} ( 5 x ) \cdot 5})

= x \to 0 lim (\frac{cos ( 7 x ) \cdot 7}{sec ^{2} ( 5 x ) \cdot 5})

Plug in the value

x = 0

= \frac{cos ( 7 \cdot 0 ) \cdot 7}{sec ^{2} ( 5 \cdot 0 ) \cdot 5}

Simplify

\frac{cos ( 7 \cdot 0 ) \cdot 7}{sec ^{2} ( 5 \cdot 0 ) \cdot 5} : \frac{7}{5}

= \frac{7}{5}

y^{^{'}} + \frac{1}{x} y - e^{- x^{2}} = 0, y (1) = 0

n = 0 \sum \infty 2^{n} n^{2} x^{n}

\int ln (3) e^{x} d x

\int \frac{x ^{4} + 9}{x ^{4} + 9 x ^{2}} d x

\frac{1}{( s + 6 ) ( s - 4 )}

What is the limit as x approaches 0 of (sin(7x))/(tan(5x)) ?
The limit as x approaches 0 of (sin(7x))/(tan(5x)) is 7/5