What is the limit as t approaches 0 of ((cos(t))/(cos(2t)))^{1/(t^2)} ?

The limit as t approaches 0 of ((cos(t))/(cos(2t)))^{1/(t^2)} is e^{3/2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as t approaches 0 of ((cos(t))/(cos(2t)))^{1/(t^2)}

t \to 0 lim ((\frac{cos ( t )}{cos ( 2 t )})^{\frac{1}{t ^{2}}})

e^{\frac{3}{2}}

Decimal

4.48168 \dots

Solution steps

t \to 0 lim ((\frac{cos ( t )}{cos ( 2 t )})^{\frac{1}{t ^{2}}})

Apply exponent rules

= t \to 0 lim (e^{\frac{1}{t ^{2}} l n (\frac{c o s ( t )}{c o s ( 2 t )})})

Apply the Limit Chain Rule:

e^{\frac{3}{2}}

= e^{\frac{3}{2}}

x \to 1 lim (x^{3} - 2 x)

x \to 0 lim (2 x^{2} - x + 4)

x \to 2 lim (a x^{2} + 2 x - 4)

x \to - 3 lim (\frac{2 x}{x + 5})

x \to 0 + lim (2 x ln (sin (x)))

What is the limit as t approaches 0 of ((cos(t))/(cos(2t)))^{1/(t^2)} ?
The limit as t approaches 0 of ((cos(t))/(cos(2t)))^{1/(t^2)} is e^{3/2}