Number and Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Evaluate limx→0+lnx1/x\lim_{x\to0^+}\frac{\ln x}{1/x}limx→0+1/xlnx
Evaluate limx→π2−π2−xcosx\lim_{x\to\tfrac{\pi}{2}^-}\frac{\tfrac{\pi}{2}-x}{\cos x}limx→2π−cosx2π−x
Evaluate limx→1xsin((x−1)2)3x−3\lim_{x\to1}\frac{x\sin\bigl((x-1)^2\bigr)}{3x-3}limx→13x−3xsin((x−1)2)
Evaluate limx→∞x3ex\lim_{x\to\infty}\frac{x^3}{e^x}limx→∞exx3
Evaluate limx→2x2lnx−4ln2x−2\lim_{x\to2}\frac{x^2\ln x - 4\ln2}{x-2}limx→2x−2x2lnx−4ln2
Evaluate limx→0tanx−xx3\lim_{x\to0}\frac{\tan x - x}{x^3}limx→0x3tanx−x
Evaluate limx→0e2x−1−2xx2\lim_{x\to0}\frac{e^{2x} - 1 - 2x}{x^2}limx→0x2e2x−1−2x
Evaluate limx→1xx−1x−1\lim_{x\to1}\frac{x^x -1}{x-1}limx→1x−1xx−1
Evaluate limx→1x1/x−1x−1\lim_{x\to1}\frac{x^{1/x} -1}{x-1}limx→1x−1x1/x−1
Evaluate limx→0sinx−x+x36x5\lim_{x\to0}\frac{\sin x - x + \tfrac{x^3}{6}}{x^5}limx→0x5sinx−x+6x3
Evaluate limx→0ln(1+3x)−sin(3x)x3\lim_{x\to0}\frac{\ln(1+3x)-\sin(3x)}{x^3}limx→0x3ln(1+3x)−sin(3x)
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Question Type 2: Computing harder derivatives from first principles