MATH1016 Revision Session

-6cos(x)sin(x)

6cos(x)

6sin(x)cos(x)

3cos(x)sin(x)

Product Rule

Quotient Rule

Tabular Integration

Chain Rule

sin(x)cos(x)

-cos(x)sin(x)

cos(x)sin(x)

cos(2x)

[-1,0]

$$\left[\frac{-\pi}{2},\frac{\pi}{2}\right]$$

[-1,1]

$$\left[\frac{-1}{2},\frac{1}{2}\right]$$

Taylor is a linear approximation and Maclaurin is a quadratic approximation

Taylor series have only two terms

Maclaurin series can have an infinite amount of terms

Maclaurin is a special case of a Taylor series that uses 0 as its single point

$$k=\frac{10}{2e}$$

$$k=\ln\left(20\right)$$

$$k=\frac{\ln\left(10\right)}{2}$$

$$k=2\ln\left(10\right)$$

log3

log6

log4

log

$$\log_x\left(\frac{x^6}{y}\right)$$

$$\log_y\left(\frac{y^6}{x}\right)$$

$$\log_xx^6$$

$$\log_x\left(\frac{x^{ }}{y}\right)$$

$$\log_a\left(m^3n^4t^5\right)$$

$$2\log_a\left(m^3n^4\right)$$

$$\log_a\left(\frac{m^4n^3}{t^5}\right)$$

$$\log_a\left(\frac{m^3n^4}{t^5}\right)$$

$$23\log x$$

$$2\log x$$

$$3\log x$$

$$\log x$$