Formulas - Math 115



Formulas

Geometry & Trigonometry:

Circles: Area = (r2 Circumference = 2(r

Spheres: Volume = (r3 Surface Area = 4(r2

Cylinders: Volume = (Area of base) ( (Height)

Cones: Volume = (Area of base) ( (Height)

sin2x + cos2x = 1 tan2x + 1 = sec2x ctn2x + 1 = csc2x

sin(x+y) = sinx cosy + cosx siny cos(x+y) = cosx cosy - sinx siny

sin 2x = 2 sinx cosx cos 2x = cos2x - sin2x

sinx siny = cosx cosy =

sinx cosy = sin2x = cos2x =

Derivatives

Linear approximation (3 ways of writing the same thing)

f(x) ( f(xo) + f’(xo)(x-xo) f(x+(x) ( f(x) + f’(x) (x (y ( (x

Quadratic approximation

f(x) ( f(xo) + f’(xo)(x-xo) + (x-xo)2 f(x+(x) ( f(x) + f’(x) (x + ((x)2

(y ( (x + ((x)2

Mean Value Theorem (Slope of secant line = slope of tangent line at intermediate point. Same as linear approximation but uncertaintly is where derivative is evaluated.)

f(x) = f(xo) + f’(c)(x-xo) f(x+(x) = f(x) + f’(c) (x ( (c)

Summation Formulas and Integrals

1 + 2 + 3 + ... + n =

12 + 22 + 32 + ... + n2 =

13 + 23 + 33 + ... + n3 =

1 + x + x2 + ... + xn =

=

Area = L(x) = Length of cross section through x.

Volume = A(x) = Area of cross section through x.

= ( For the solid created by rotating a region about the x axis. The region is bounded above by y = f(x), below by y = g(x), on the left by x = a and on the right by x = b.

Volume = 2( For the solid created by rotating the same region about the y axis.

Work = F(x) = Force on object at position x.

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