State multiplication working rule of limit.

1.	State multiplication working rule of limit.
Answer» f(x) and g (x) are two functions of real variable x and \(\lim\limits_{x\to a}\) f(x) = 1,\(\lim\limits_{x\to a}\) g (x) = m. If f (x) g ∙ (x) is the product of two functions, then multiplication working rule of limit is as follows: \(\lim\limits_{x\to a}\,[f(x).g(x)]\\=\lim\limits_{x\to a}f(x).\lim\limits_{x\to a}\,g(x)\\=l\times m\) Thus, limit of product of two functions is equal to the product of limit of these two functions.

Answer»

f(x) and g (x) are two functions of real variable x and \(\lim\limits_{x\to a}\) f(x) = 1,\(\lim\limits_{x\to a}\) g (x) = m.

If f (x) g ∙ (x) is the product of two functions, then multiplication working rule of limit is as follows:
\(\lim\limits_{x\to a}\,[f(x).g(x)]\\=\lim\limits_{x\to a}f(x).\lim\limits_{x\to a}\,g(x)\\=l\times m\)

Thus, limit of product of two functions is equal to the product of limit of these two functions.

Discussion

No Comment Found

Related InterviewSolutions

Evaluate `lim_(xrarr0)((3^(2x)-1)/(2^(3x)-1)).`
Show that `lim_(xrarr2)(x)/([x])` does not exist.
If `y(x)=|x|-3, "find"lim_(xrarr3)f(x).`
Evaluate the following limits: `lim_(xrarr0)((1-cosx))/(sin^(2)x)`
Evaluate the following limits: `lim_(xrarr0)(cos2x-1)/(cosx-1)`
Evaluate the following limits: `lim_(xrarr0)(ax+x cosx)/(b sinx)`
Evaluate `(i)lim_(xrarr0)((1-cos 4x)/(1-cos5x))` `(ii) lim_(xrarr0)((1-cosmx)/(1-cosnx)).`
Evaluate `lim_(xrarr0)((1-cosx))/(x^(2)).`
Evaluate the following limits: `lim_(xrarr0)(1-cos2mx)/(1-cos2nx)`
For ` x in R , lim_( x to infty) ((x -3)/(x + 2))^x ` is equal toA. eB. `e^(-1)`C. ` e^(-5)`D. `e^(5)`

State multiplication working rule of limit.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment