Calculus Topics - GATE CS & IT Syllabus

1

Value that a function approaches as input approaches some point.

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📌 Key FormulaL'Hôpital's rule: lim f/g = lim f'/g' if 0/0 or ∞/∞.

2

Function is continuous if limit equals function value at that point.

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📌 Key FormulaContinuous at x=a if lim_{x→a} f(x) = f(a).

3

Existence of derivative at a point, representing slope of tangent.

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📌 Key Formulaf'(a) = lim_{h→0} (f(a+h)-f(a))/h.

4

Rolle's theorem, Lagrange's MVT, Cauchy's theorem.

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📌 Key FormulaLagrange: f'(c) = (f(b)-f(a))/(b-a) for some c in (a,b).

5

Finding local/global extreme values using derivatives.

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📌 Key FormulaFirst derivative test, second derivative test: f''(c)>0 → local min.

6

Definite and indefinite integrals; area under curve.

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📌 Key Formula∫ x^n dx = x^{n+1}/(n+1) + C; ∫ e^x dx = e^x + C; ∫ 1/x dx = ln|x| + C.