Limits of Rational Functions
Read this topicExplanations 8
- A rational function is essentially any function that can be expressed as a rational function. For example::: y=x(10x20)y=\frac{\sqrt{x}}{(10x^{20})}y=(10x20)x
By Ryan Jiang, Evan Tong
- (Video) Calculating a Limit by Factoring and Canceling by PatrickJMT Here's a video by patrickJMT showing you how to find a limit of a function using the factor canceling techni…
By Alex Federspiel
- (Video) Calculating a Limit by Expanding and Simplifying by PatrickJMT Here's a video by patrickJMT showing you how to find a limit of a function using the expanding and simplif…
By Alex Federspiel
- (Video) Calculating a Limit by Getting a Common Denominator by PatrickJMT Here's a video by patrickJMT showing you how to find the limit of a function using the common denominat…
By Alex Federspiel
- (Videos) Calculating a Limit by Multiplying by a Conjugate by PatrickJMT Here's a video by patrickJMT showing you how to find the limit of a function using the conjugate techniq…
By Alex Federspiel
- (Video) Limits at Infinity by PatrickJMT Here's a video by patrickJMT showing you how to find limits of functions as they approach infinity. When we take a limit as it approache…
By Alex Federspiel
- By representing a function as a table and plugging in x and y values, we are able to intuitively find the limit that the function approaches. Similarly, we are able to assess wh…
By Elise
- (Video) Limits Involving Absolute Value by PatrickJMT Here's a video by patrickJMT showing you how to find the limit of function with absolute values. The example he looks at is…
By Alex Federspiel
Problems 28
- limx→3f(x)=(3)/(9−x2)−(x)/(9−x2)\lim_{x \rightarrow 3} f(x) = (3)/(9-x^2) - (x)/(9-x^2)limx→3f(x)=(3)/(9−x2)−(x)/(9−x2)
- limx→3f(x)=(x3)/(x2−6)\lim_{x \rightarrow 3} f(x) = (x^3)/(x^2 - 6)limx→3f(x)=(x3)/(x2−6)
- limx→−3f(x)=(x2−x)/(x+3)\lim_{x \rightarrow -3} f(x) = (x^2 - x)/(x + 3)limx→−3f(x)=(x2−x)/(x+3)
- limx→4f(x)=(x2−3x−4)/(x−4)\lim_{x \rightarrow 4} f(x) = (x^2 - 3x - 4)/(x-4)limx→4f(x)=(x2−3x−4)/(x−4)
- Compute limx→4x2−3x−4(x−4)(x+1)\displaystyle\lim_{x \rightarrow 4} \frac{x^2 - 3x - 4}{(x-4)(x+1)}x→4lim(x−4)(x+1)x2−3x−4.
- limx→−8f(x)=(x2+7x−8)/((x+8)(x+1))\lim_{x \rightarrow -8} f(x) = (x^2 + 7x - 8)/((x+8)(x+1))limx→−8f(x)=(x2+7x−8)/((x+8)(x+1))
- Evaluate limx→3x2+x−12x−3.\lim_{x\to3}\frac{x^2+x-12}{x-3}.x→3limx−3x2+x−12.
- Evaluate limx→−515+1x5+x\lim_{x\to-5}\frac{\frac15+\frac1x}{5+x}x→−5lim5+x51+x1
- Evaluate limx→0(4+x)−1−4−1x\lim_{x\to0}\frac{(4+x)^{-1}-4^{-1}}{x}x→0limx(4+x)−1−4−1
- Evaluate limx→1x2+3x−4x3−3x2−22x+24\lim_{x\to1}{\frac{x^2+3x-4}{x^3-3x^2-22x+24}}x→1limx3−3x2−22x+24x2+3x−4
- Evaluate limx→9x−9x−3\lim_{x\to9}{\frac{x-9}{\sqrt{x}-3}}x→9limx−3x−9
- Evaluate limx→1x−1x3−1\lim_{x\to1}{\frac{x-1}{\sqrt[3]{x}-1}}x→1lim3x−1x−1
- Evaluate limx→2+x2−4∣x−2∣\lim_{x\to2^+}{\frac{x^2-4}{|x-2|}}x→2+lim∣x−2∣x2−4
- Evaluate limx→2−x2−4∣x−2∣\lim_{x\to2^-}{\frac{x^2-4}{|x-2|}}x→2−lim∣x−2∣x2−4
- Evaluate limx→∞4x3−2x2+6−x3+8\lim_{x\to\infty}{\frac{4x^3-2x^2+6}{-x^3+8}}x→∞lim−x3+84x3−2x2+6
- Evaluate limx→∞8x2+4x−32x3+7x−2\lim_{x\to\infty}{\frac{8x^2+4x-3}{2x^3+7x-2}}x→∞lim2x3+7x−28x2+4x−3
- Evaluate limx→∞4x−6x3+11+14x4−22x215+6x+2x4−8x3\lim_{x\to\infty}{\frac{4x-6x^3+11+14x^4-22x^2}{15+6x+2x^4-8x^3}}x→∞lim15+6x+2x4−8x34x−6x3+11+14x4−22x2
- Evaluate limx→ex2−e22x−2e\lim_{x\rightarrow e}\frac{x^2-e^2}{2x-2e}x→elim2x−2ex2−e2
- Evaluate the following expression: limx→2x−2x2−4\lim_{x \to 2} \frac{x-2}{x^2-4}limx→2x2−4x−2
- Evaluate limn→0xx+1−1\lim_{n\to0}\frac{x}{\sqrt{x+1}-1}n→0limx+1−1x
- Evaluate limx→∞x2+3−x2+1\lim_{x\to\infty}{\sqrt{x^2+3}-\sqrt{x^2+1}}x→∞limx2+3−x2+1
- Evaluate limx→∞(x+1x−1)x\lim_{x\to\infty}(\frac{x+1}{x-1})^xx→∞lim(x−1x+1)x
- Find the limit of the function algebraically. When finished, construct a table of the function with x and y values to assess whether or not you are correct. Find the limit as x …
- Gabriel's Horn is defined as the shape generated when we revolve the graph of y=1xy = \frac{1}{x}y=x1 around the xxx-axis for x≥1.x \geq 1.x≥1. What is the volume of Gabriel's …
- We define Gabriel's Modified Horn as the shape generated when we revolve the graph of y=1xαy = \frac{1}{x^{\alpha}}y=xα1 around the xxx-axis for x≥1,x \geq 1,x≥1, where α>12\al…
- We define Gabriel's Modified Horn as the shape generated when we revolve y=1xαy = \frac{1}{x^{\alpha}}y=xα1 around the xxx-axis for x≥1,x \geq 1,x≥1, where α>12\alpha > \frac{1…
- We define Gabriel's Modified Horn as the shape generated when we revolve y=1xαy = \frac{1}{x^{\alpha}}y=xα1 around the xxx-axis for x≥1,x \geq 1,x≥1, where α>12\alpha > \frac{1…
- We define Gabriel's Modified Horn as the shape generated when we revolve the graph of y=1xαy = \frac{1}{x^{\alpha}}y=xα1 around the xxx-axis for x≥1,x \geq 1,x≥1, where α>12\al…