Jeopardy 1007

Differentiate the following:

100

Differentiate 2x⁵ + 3x³ + 45x + 2

10x⁴ + 9x² + 45

200

e^4x

4e^4x

300

y = (5e^4x + 2x)(x⁴)(2x)

(20e^4x + 2)(x⁴)(2x) + (5e^4x + 2x)(4x³)(2x) + (5e^4x + 2x)(x⁴)(2)

400

y = ln(x²) / (2x + 1)

2x(2x+1) - 2x²ln(x²) / ( x²)(2x + 1)²

500

y = ln(sec²x) + sin(e^{3x + 1}) / x² + cosx

2tanx + [cos(e^{3x + 1})(3e^{3x + 1})(x² + cosx) - sin(e^{3x + 1})(2x - sinx)] / (x² + cosx)²

Limits, Horizontal Asymptotes etc

100

Find lim x->oo (e^1/x)

1

200

Find lim x->oo (5x² + 8x - 3) / 3x² + 2

5/3

300

Find the horizontal asymptote of y= (x³ - 2) / (|x³| + 1)

y = 1 and y = -1

400

Find lim x->0^- (e^1/x)

0

500

Find the horizontal asymptote(s) of f(x) = (x² + 1)^1/2 / (x+1)

y = 1

Vertical Asymptotes

100

What is the vertical asymptote(s) of y = (x + 3) / (x + 4)

x = -4

200

Find the V.A of f(x) = e^1/x + 6x²

NONE!!!

300

Find the V.A of y = -1 / (x³ + x²)

x = 0 and x = -1

400

Find lim x->0⁺ (x²/2 - 1/x)

0

500

lim x->2 (x² - 3x + 2)/ (x³ - 2x²)

1/4

Trig! Find the derivative of:

100

y = 5cos(x³)

-5sin(x³)(3x²)

200

y = 5e^3x + sinxcosx

15e^3x + (cosx)² - (sinx)²

300

y = csc(ln2x)

-csc(ln2x)cot(ln2x)(2/2x)

400

y = sec²(4x+2) + (tanx)x²

8[sec(4x + 2)]²tan(4x+2) + sec²x(x²) + 2x(tanx)

500

y = ln(5cot3x)/(4x+2sinx)²

something.... let's write it out