Topics

More AI tools from SnapXam

Exercise

$\lim_{x\to\infty}\left(\frac{x^2+2x+6}{2x-1}\right)$

Step-by-step Solution

1

As it's an indeterminate limit of type $\frac{\infty}{\infty}$, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is

$\lim_{x\to\infty }\left(\frac{\frac{x^2+2x+6}{x}}{\frac{2x-1}{x}}\right)$
2

Separate the terms of both fractions

$\lim_{x\to\infty }\left(\frac{\frac{x^2}{x}+\frac{2x}{x}+\frac{6}{x}}{\frac{2x}{x}+\frac{-1}{x}}\right)$
3

Simplify the fraction

$\lim_{x\to\infty }\left(\frac{\frac{x^2}{x}+2+\frac{6}{x}}{2+\frac{-1}{x}}\right)$
4

Simplify the fraction $\frac{x^2}{x}$ by $x$

$\lim_{x\to\infty }\left(\frac{x+2+\frac{6}{x}}{2+\frac{-1}{x}}\right)$
5

Evaluate the limit $\lim_{x\to\infty }\left(\frac{x+2+\frac{6}{x}}{2+\frac{-1}{x}}\right)$ by replacing all occurrences of $x$ by $\infty $

$\infty $

Final answer to the exercise

$\infty $

Try other ways to solve this exercise

  • Choose an option
  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Load more...
Can't find a method? Tell us so we can add it.

Similar Questions Solved

$\lim_{x\to\infty}\left(\frac{\sqrt{x^2+1}}{x}\right)$

$\lim_{x\to\infty}\left(\frac{ax^4+bx^2+c}{dx^3+ex^2+fx+g}\right)$

$\lim_{x\to\infty}\left(\frac{7x^2}{x-x^3}\right)$

$\lim_{x\to-3}\left(\frac{x^4-81}{x+3}\right)$

$\lim_{x\to-1}\left(\frac{12x^3+12x^2}{x^4-x^2}\right)$

$\lim_{x\to1}\left(\frac{x^3-1}{4x^3-x-3}\right)$

$\lim_{x\to8}\left(\frac{x-8}{x^2-64}\right)$

Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

Related Topics

Symbolic mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Empowering students and teachers through AI

By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot your password?

Empowering students and teachers through AI



Register here if you don't have an account.
Forgot your password?

Your Personal Math Tutor. Powered by AI

Available 24/7, 365 days a year.

Complete step-by-step math solutions. No ads.

Choose between multiple solving methods.

Download unlimited solutions in PDF format.

Premium access on our iOS and Android apps.

Join 1M+ students worldwide in problem solving.

Choose the plan that suits you best:
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account