Question

!! AP CALCULUS AB !!

find the limit of [(secx*sinx) + (cscx*cosx)]/(3secx) as x approaches 3pi/2

Answer 1

`f(x)= \frac{(sin(x))/(cos(x))+(cos(x))/(sin(x))}{3\sec{x}}`

`\frac{(sin(x))/(cos(x))+(cos(x))/(sin(x))}{3\sec{x}} \implies \\ \frac{\sin^2{x}+\cos^2{x}}{sin(x)cos(x)}(cos(x))/(3)\implies \\(1)/(sin(x)cos(x))*(cos(x))/(3)\implies \\ (1)/(3sin(x))`

So,

`\lim_{x \rightarrow (3\pi)/(2)}{f(x)=f((3\pi)/(2))=\frac{1}{3\sin{(3\pi)/(2)}}=-(1)/(3)`