Praxis 5165 Questions and Answers Graded A

Praxis 5165 Questions and Answers Graded A Integration by parts formula ∫udv= uv-∫vdu 1 + tan^2x = sec^2x 1 + cot^2x = csc^2x sin^2x + cos^2x = 1 Slope Intercept Form y=mx+b Point Slope Form y-y₁=m(x-x₁) Discriminant b²-4ac If b²-4ac > 0 There are 2 real roots If b²-4ac < 0 There are no roots If b²-4ac = 0 1 real root Distance between two points d = √(x₁-x₂)² + (y₁-y₂)² Volume of a Sphere Formula V=4/3πr³ Surface Area of a Sphere SA=4πr² Volume of a Cylinder Formula V=πr²h Surface Area of a Cylinder SA=2πrh + 2πr² Volume of a Cone V = 1/3πr²h Surface Area of a Cone SA = πrs+πr² Volume of a Rectangular Prism V=lwh Volume of a Triangular Prism V=(1/2bh)h Circumference of a Circle C=2πr Area of a Circle A=πr² Continuous compounding interest B=Peʳᵗ B=final balance P=principal deposit r=interest rate t=time Compounding interest annually B=P(1+r)ᵗ P=principal r=annual interest ratet=time B=ending balance wanted Length of an arc (central angle/360) x 2πr d/dx (a^x) a^x ln(a) d/dx (log_a (x)) = 1/(x ln a) d/dx (sin x) cos x d/dx (cos x) -sin x d/dx (tan x) sec^2x d/dx (sec x) sec x tan x d/dx (csc x) -csc x cot x d/dx (cot x) -csc^2 x d/dx [f(x)*g(x)] f(x)g'(x) + g(x)f'(x) d/dx [f(x)/g(x)] g(x)f'(x)- f(x)g'(x)/g(x)^2 d/dx (sin^-1 x) 1/√(1-x^2) d/dx (cos^-1 x) - [1/√(1-x^2)] d/dx (tan^-1 x) 1/(1 + x^2) If y is a function of x, then ... each value of x in the domain is mapped to at most one value of y.