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

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

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limit as x approaches 0 of (cos(7x)tan(7x))/x

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

7

Solution steps

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

cos (7 x) tan (7 x) = sin (7 x)

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 7 x ) \cdot 7}{1})

= x \to 0 lim (\frac{cos ( 7 x ) \cdot 7}{1})

Plug in the value

x = 0

= \frac{cos ( 7 \cdot 0 ) \cdot 7}{1}

Simplify

\frac{cos ( 7 \cdot 0 ) \cdot 7}{1} : 7

= 7

f (x) = (1 + x) cos (x), at x = 0

y = \frac{1}{3} x^{2} - 2 x + 4, (3, 1)

\frac{d}{d x} (cos (tan (4 x)))

\frac{d}{d x} (\frac{x ^{3} - 6 x ^{2} + 5}{x})

n = 0 \sum \infty (\frac{1}{6})^{n}

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