MTH253- Calculus 3 Midterm

formulas

### **Linear Approximation of a Function at a Point**

y= f(a)+ f'(a)(x−a)

differential form

dy = f’(x) dx

Newton’s method

xₙ₊₁ = xₙ - (f(xₙ) / f’(xₙ))

A **separable differential equation** is any equation that can be written in the form

y'=f(x)g(y) or y’ = f(x)/ g(y)

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Newton’s law of cooling (1)

dT/dt = k(T-Ts)

Newton’s law of cooling (2)

T(t) = (To - Ts)e^kt + Ts

∫csc²(x) dx =

-cot(x) +C

infinite sequence form:

a1, a2, a3…., an

sequence notation

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