Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

f(x)=(x^(3)-1)/(x-1) Dapatkan lim_(x rarr1)f(x). Buatlah sketsa grafik y=f(x).

f(x)=x3−1x−1 f(x)=\frac{x^{3}-1}{x-1} \newlineDapatkan lim⁡x→1f(x) \lim _{x \rightarrow 1} f(x) .\newlineBuatlah sketsa grafik y=f(x) y=f(x) .

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Solve radical equationsright chevron icon

Full solution

Q. f(x)=x3−1x−1 f(x)=\frac{x^{3}-1}{x-1} \newlineDapatkan lim⁡x→1f(x) \lim _{x \rightarrow 1} f(x) .\newlineBuatlah sketsa grafik y=f(x) y=f(x) .
  1. Factor Numerator: Factor the numerator of f(x)f(x) to simplify the expression.f(x)=x3−1x−1=(x−1)(x2+x+1)x−1f(x) = \frac{x^3 - 1}{x - 1} = \frac{(x - 1)(x^2 + x + 1)}{x - 1}
  2. Cancel Terms: Cancel out the (x−1)(x - 1) terms.\newlinef(x)=x2+x+1f(x) = x^2 + x + 1
  3. Substitute x=1x = 1: Substitute x=1x = 1 into the simplified function to find the limit.lim⁡x→1f(x)=12+1+1=3\lim_{x \to 1} f(x) = 1^2 + 1 + 1 = 3
  4. Sketch Graph: Sketch the graph of y=f(x)=x2+x+1y = f(x) = x^2 + x + 1. This is a parabola opening upwards with vertex at (−0.5,0.75)(-0.5, 0.75).

More problems from Solve radical equations

Question
What is the domain of this function? \newliney=xy = \sqrt{x} \newlineChoices: \newline{x∣x≥0}\{x|x \geq 0\}\newline{x∣x≤0}\{x|x \leq 0\}\newline{x∣x<0}\{x | x < 0\}\newline{x∣x>0}\{x|x>0\}
Get tutor helpright-arrow

Posted 3 months ago

Question
Find the real-number root. \newline16\sqrt{16}\newline\newlineWrite your answer in simplified form. \newline____\_\_\_\_
Get tutor helpright-arrow

Posted 3 months ago

Question
Find the real-number root. \newline916\sqrt{\frac{9}{16}}\newlineSimplify your answer and write it as a decimal or as a proper or improper fraction.\newline_____\_\_\_\_\_
Get tutor helpright-arrow

Posted 3 months ago

Question
Find the real-number root using a calculator. Round your answer to the nearest thousandth. \newline`\sqrt{957} `\newline _______
Get tutor helpright-arrow

Posted 3 months ago

Question
Multiply. Write your answer in simplest form. \newline273×42\sqrt{273} \times \sqrt{42}\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Simplify. \newline634\sqrt{\frac{63}{4}}\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Simplify. Rationalize the denominator.\newline−49−2\frac{-4}{9 - \sqrt{2}}\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for z z .\newline16=z 16 = \sqrt{z} \newlinez= z = _____
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for p p .\newline8=p 8 = \sqrt{p} \newlinep= p = _____
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for p p .\newline4p=10+3p \sqrt{4p} = \sqrt{10 + 3p} \newlinep= p = _____
Get tutor helpright-arrow

Posted 3 months ago

View all (187)