What is the limit as t approaches 0 of (3/(tsqrt(1+t)))-3/t ?

The limit as t approaches 0 of (3/(tsqrt(1+t)))-3/t is -3/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as t approaches 0 of (3/(tsqrt(1+t)))-3/t

t \to 0 lim ((\frac{3}{t 1 + t}) - \frac{3}{t})

- \frac{3}{2}

Decimal Notation

- 1.5

Solution steps

t \to 0 lim (\frac{3}{t 1 + t} - \frac{3}{t})

Rationalize numerator

\frac{3}{t 1 + t} - \frac{3}{t} : - \frac{3}{( t + 1 + 1 ) t + 1}

= t \to 0 lim (- \frac{3}{( t + 1 + 1 ) t + 1})

Plug in the value

t = 0

= - \frac{3}{( 0 + 1 + 1 ) 0 + 1}

(0 + 1 + 1) 0 + 1 = 2

= - \frac{3}{2}

\int 2 + 4 y^{2} d y

\frac{d}{d x} (x 49 - x^{2})

\int x^{2} + 5 d x

\int \frac{1}{8 - 6 x - 9 x ^{2}} d x

\frac{x ^{2} + sec ( x )}{x - 2 e ^{x}}

What is the limit as t approaches 0 of (3/(tsqrt(1+t)))-3/t ?
The limit as t approaches 0 of (3/(tsqrt(1+t)))-3/t is -3/2