# Honors Pre-Calculus

## 151 terms · Final Review

y'=x²e^x + 2xe^x

### y=7/(x²+9)

y'=(-14x)/(x²+9)²

### y=sinx(x²+3x+5)

y'=(2x+3)sinx+cosx(x²+3x+5)

y'=sinπ(2x+3)

y'=2xe²

y'=14x

### y=sinx / (x²+3x+5)

y'=((x²+3x+5)(cosx)-sinx(2x+3))/(x²+3x+5)²

y'=7/x³

y'=2e^x

y'=1/(2e√x)

y'=2π

y'(1/8)=66

y'(1/8)=0

y'(4)=25

### y=2sinxcosx

y'=-2sin²x+2cos²x

y'=2

none of these

### y=cosx(x²+3x+5)

y'=cosx(2x+3) - sinx (x²+3x+5)

### y=(x²+3x+5)/cosx

y'=((cosx)(2x+3)+(x²+3x+5)sinx)/ cos²x

y'=e/(2√x)

1

√3/2

√2/2

1/2

-1/2

-√2/2

-√3/2

-1

-√3/2

-√2/2

-1/2

1/2

√2/2

√3/2

1

1/2

√2/2

√3/2

1

√3/2

√2/2

1/2

-1/2

-√2/2

-√3/2

-1

-√3/2

-√2/2

-1/2

√3/3

1

√3

U

-√3

-1

-√3/3

√3/3

1

√3

U

-√3

-1

-√3/3

1

(log₆4)/3

(ln3)/3

0

(ln4)/2

ln5+1

no solution

2/5

2

1

3/7

x=3

3n

3n

5

x=6

x=3

x=4

x=-3

x=81

x=125

e⁸

100/3

9

10⁶/7

(e³+1)\2

e-1

2

1

2/5

4/5

period

frequency

Arcsine

- sine

### cosine

The cofunction of sine

2

1

### How could you affect the amplitude of a graph made by a tuning fork?

Make the sound of the fork louder

### How could you affect the period of a graph made by a tuning fork?

Get a tuning fork with a different frequency.

### If the period of the graph of a tuning fork is larger

The frequency of the tuning fork is smaller.

infinite

### How do you calculate the amplitude from a set of sinusoidal data?

Take the highest minus the lowest value and divide by 2

arcsin 0

arcsin ½

arcsin(½√2)

arcsin(½√3)

arcsin 1

arcsin(-1)

arcsin(-½√3)

arcsin(-½√2)

arcsin(-½)

arcsin 2

arcsin(-3)

arctan 0

arctan(⅓√3)

arctan 1

arctan(√3)

arctan(-√3)

arctan(-1)

arctan(-⅓√3)

arccos 1

arccos(½√3)

arccos(½√2)

arccos ½

arccos 0

arccos(-½)

arccos(-½√2)

arccos(-½√3)

arccos(-1)

arccos(-2)

arccos(√3)

arcsec 1

arcsec 2

arcsec(√2)

arcsec(-2)

arcsec(-√2)

arcsec(-1)

### y=2sin(2x)+3

Period = pi, Amplitude = 2, Vertical Shift up 3

### y=2sin 2( x +3 )

Period = pi, Amplitude = 2, Horizontal Shift 3 left

### y = -2 sin ( x ) + 3

Period = 2pi, Amplitude = 2, Vertical Shift up 3, flip over the x-axis

### y=2sin(2x+3)

Period = pi, Amplitude = 2, Horizontal Shift 3/2 left

### y=2sin(-x)+3

Period = 2pi, Amplitude = 2, Up three, Flips over the y-axis

### y=-2cos(3x)

Amplitude = 2, Flip over the x-axis, Frequency = 3/2pi

### y=2cos(3x+pi)

Period = 2pi/3, Amplitude = 2, Phase Shift pi/3

### y=3cos(2x)+1

Period = pi, Amplitude = 3, Vertical Shift up 1

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