If Lim(xto0)(1+x+(f(x))/x)^(1//x)=e^(3),...

If `Lim_(xto0)(1+x+(f(x))/x)^(1//x)=e^(3)`, then show that `Lim_(xto0)(f(x))/x^(2)=2`.

Promotional Banner

Promotional Banner

Topper's Solved these Questions

LIMITS
AAKASH SERIES|Exercise EXERCISE-2.1 (VERY SHORT ANSWER QUESTIONS)|20 Videos
LIMITS
AAKASH SERIES|Exercise EXERCISE-2.1 (SHORT ANSWER QUESTIONS)|17 Videos
LIMITS
AAKASH SERIES|Exercise PRACTICE EXERCISE|143 Videos
INVERSET TRIGONOMETRIC FUNCTIONS
AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL-II PRACTICE SHEET (ADVANCED) INTEGER TYPE QUESTIOS)|5 Videos
LOCUS
AAKASH SERIES|Exercise PRACTICE EXERCISE|37 Videos

AAKASH SERIES-LIMITS-SOLVED EXAMPLE

Find Lt(xtooo)((x+a)/(x+b))^(x), a, b are constants.
Text Solution
|
Evaluate Lt(xtooo)((x^(2)+ax+b)/(x^(2)+cx+d))^(x) where a, b, c, d are...
Text Solution
|
Find Lt(xtooo)((3x^(2)+1)/(4x^(2)-1))^((x^(3))/(1+x))
Text Solution
|
Evaluate Lt(xto0)((a^(x)+b^(x)+c^(x))/3)^(1/x) where a,b,cinR^(+).
Text Solution
|
If Lt(xto0)(1+ax+bx^(2))^(2//x)=e^(3), find a and b.
Text Solution
|
Find Lt(xto0)((sinx-x+x^(3)/6)/x^(5))
Text Solution
|
Find a, b and c if Lt(xto0)((ae^(x)-bcosx+ce^(-x))/x^(2))=2
Text Solution
|
Evaluate Lt(xto0)(((1+x)^(1/x)-e+(ex)/2)/(x^(2)))
Text Solution
|
Find Lt(xtooo)([ax+b])/x(agt0). Where [.] denotes GIF.
Text Solution
|
Show that Lt(ntooo)([x]+[2x]+...+[nx])/n^(2)=x/2.
Text Solution
|
Show that Lt(xtooo)(x-logx)/(x+logx)=1.
Text Solution
|
Show that Lt(xtooo)(2x+7sinx)/(4x+3cosx)=1/2
Text Solution
|
Show that Lt(xto0)(e^(x)-1)/x=1
Text Solution
|
Find Lt(xto0)(1-cosx)/x^(2)
Text Solution
|
Evaluate Lt(xtoa)(x^(a)-a^(x))/(x^(x)-a^(a))
Text Solution
|
Find Lt(xtooo)(logx)/x
Text Solution
|
If underset(x to 0)"Lt" ((cos 4x+a cos 2x+b)/(x^(4))) is finite, then...
Text Solution
|
Show that Lim(ntooo)prod(r=1)^(n)r/(r^(4)+r^(2)+1)=1/2
Text Solution
|
ABC is an isosceles triangle inscribed in a circle of unit radius. AB ...
Text Solution
|
If Lim(xto0)(1+x+(f(x))/x)^(1//x)=e^(3), then show that Lim(xto0)(f(x)...
Text Solution
|