Limits of Products and Quotients
Read this topicExplanations 3
- There is a special property of limits pertaining to products: limx→h(f(x)g(x))=limx→h(f(x))limx→h(g(x)).\begin{equation} \lim_{x \rightarrow h}(f(x)g(x)) = \lim_{x \rightarro…
By Joshua Siktar, Ritesh Ragavender, Alex Federspiel
- There is a special property of limits pertaining to products: limx→h(f(x)g(x))=limx→h(f(x))⋅limx→h(g(x))\lim_{x \rightarrow h}(f(x)g(x)) = \lim_{x \rightarrow h}(f(x)) \cdot …
By Joshua Siktar, Victor Wang, Moor Xu
- (Videos) Limit Laws to Evaluate a Limit by PatrickJMT Here's a video by patrickJMT where he goes over problems which can be solved using the limit laws. Suppose that ccc is a co…
By Alex Federspiel
Problems 9
- Find limx→3x2+3x+2x2−6x+12\lim_{x\to3}{\dfrac{x^2+3x+2}{x^2-6x+12}}x→3limx2−6x+12x2+3x+2
- Find limx→1xln(x)cos(x)\lim_{x\to1}{\sqrt{x}\ln(x)\cos(x)}x→1limxln(x)cos(x)
- Find limx→3x2−x−12x−3\lim_{x\to3}{\dfrac{x^2-x-12}{x-3}}x→3limx−3x2−x−12
- Find limx→−1cos(x)(x−1)xex\lim_{x\to-1}{\cos(x)(x-1)\sqrt{x}e^x}x→−1limcos(x)(x−1)xex
- Find limx→2ln(x)(x−2)2\lim_{x\to2}{\frac{\ln(x)}{(x-2)^2}}x→2lim(x−2)2ln(x)
- Find limx→11π4sin(x)cos(x−π4)⋅tan(x−π2)csc(x−3π4)⋅sec(x−π)cot(x−5π4)\begin{array}{rl} \lim_{x\to\frac{11\pi}{4}}&{\sin(x)\cos(x-\frac{\pi}{4})}\\ &\cdot\tan(x-\frac{\pi}2…
- Given 3 functions f(x)=cos(x)f(x) = \cos(x)f(x)=cos(x), g(x)=sin(5x)+3g(x) = \sin(5x) + 3g(x)=sin(5x)+3, and a continuous function h(x)h(x)h(x) defined on all real numbers. If…
- Evaluate limx→6x2x\lim_{x\rightarrow6}\frac{\sqrt{x}}{2^x}x→6lim2xx
- Evaluate limx→2(3x+4)(9−2x)\lim_{x\rightarrow2}(3x+4)(9-2x)x→2lim(3x+4)(9−2x)