Number and Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Compute limx→01−cosxx2\lim_{x\to0}\frac{1-\cos x}{x^2}limx→0x21−cosx
Compute limx→0ln(1+x)−xx2\lim_{x\to0}\frac{\ln(1+x)-x}{x^2}limx→0x2ln(1+x)−x
Find limx→0tanx−xx3\lim_{x\to0}\frac{\tan x - x}{x^3}limx→0x3tanx−x
Evaluate limx→0ex−1−xx2\lim_{x\to0}\frac{e^x -1 - x}{x^2}limx→0x2ex−1−x
Evaluate the limit limx→0x−sinxx3\lim_{x\to 0}\frac{x - \sin x}{x^3}limx→0x3x−sinx
Evaluate limx→0ln(1+x)−x+x22x3\lim_{x\to0}\frac{\ln(1+x)-x+\tfrac{x^2}{2}}{x^3}limx→0x3ln(1+x)−x+2x2
Find limx→0ex−1−x−x22x3\lim_{x\to0}\frac{e^x -1 - x - \tfrac{x^2}{2}}{x^3}limx→0x3ex−1−x−2x2
Find limx→03x−1−xln3x2\lim_{x\to0}\frac{3^x -1 - x\ln 3}{x^2}limx→0x23x−1−xln3
Evaluate limx→01+x3−1−x3x2\lim_{x\to0}\frac{\sqrt[3]{1+x} -1 - \tfrac{x}{3}}{x^2}limx→0x231+x−1−3x
Compute limx→0(ex−1)2−x2x3\lim_{x\to0}\frac{(e^x -1)^2 - x^2}{x^3}limx→0x3(ex−1)2−x2
Find limx→01−cosx−x22x4\lim_{x\to0}\frac{1-\cos x-\tfrac{x^2}{2}}{x^4}limx→0x41−cosx−2x2
Evaluate limx→0sinx−x+x36x5\lim_{x\to0}\frac{\sin x - x + \tfrac{x^3}{6}}{x^5}limx→0x5sinx−x+6x3
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Question Type 2: Computing harder derivatives from first principles
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Question Type 4: Finding parameter values so that a limit exists (using L’Hôpital)