Excel in math and science.

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Calculus

Curve Sketching

Concept Quizzes

Curve Sketching Warmup
Turning Points
Curve Sketching
Increasing / Decreasing Functions
Vertical Asymptotes
Relative Magnitude of Functions
Tangent to a Curve
Normal to a Curve

Challenge Quizzes

Curve Sketching: Level 3 Challenges
Curve Sketching: Level 4 Challenges

Relative Magnitude of Functions

If $x$ goes to infinity, which of the following is the largest of all:

$\begin{array}{c}&\frac{x-3}{3x}, &3\sin\frac{1}{x}, &\cos \frac{1}{x}? \end{array}$

\displaystyle{ {3}\sin\frac{1}{x}}

\displaystyle{ \cos \frac{1}{x} }

\displaystyle{ \frac{x-{3}}{{3}x}}

unknown

Show explanation

View wiki

by Brilliant Staff

Which of the following is larger in the limit as $x$ grows to infinity?

$\begin{array}{c}&\sqrt{\lfloor 4x^2+9x \rfloor}, &2x \end{array}$

Details and assumptions

The function $\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}$ refers to the greatest integer smaller than or equal to $x$ . For example $\lfloor 2.3 \rfloor = 2$ and $\lfloor -5 \rfloor = -5$ . This is called the greatest integer function or the floor function.

equal

\displaystyle{\sqrt{\lfloor{4}x^2+{9}x\rfloor}}

{2}x

unknown

Show explanation

View wiki

by Brilliant Staff

Which of the following functions is largest for large positive values of $x$

$\begin{array}{c}&5x^2-2x+2, &4x^2-4x+3, &8x+7? \end{array}$

unknown

\displaystyle{ {4}x^2-{4}x+3 }

\displaystyle{ {5}x^2-{2}x+2 }

\displaystyle{ {8}x+7 }

Show explanation

View wiki

by Brilliant Staff

If $x$ goes to infinity, which of the following is the largest of all:

$\begin{array}{c}&\sqrt[x]{6^x+2^x}, &\sqrt[x]{5^x+4^x}, &\sqrt[x]{7^x}? \end{array}$

unknown

\displaystyle{ \sqrt[x]{{5}^x+{4}^x} }

\displaystyle{ \sqrt[x]{{6}^x+{2}^x} }

\displaystyle{ \sqrt[x]{{7}^x} }

Show explanation

View wiki

by Brilliant Staff

If $x$ goes to infinity, which of the following is the largest of all:

$\begin{array}{c}&x\sqrt[x]{2}, &4x, &x\sin \frac{2}{x}? \end{array}$

unknown

\displaystyle{{4}x }

\displaystyle{x\sqrt[x]{2} }

\displaystyle{x\sin \frac{{2}}{x} }

Show explanation

View wiki

by Brilliant Staff