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10 questions
The derivative of a function is its
Slope
Maximum/Minimum
Instantaneous rate of change
Common Denominator
15x2
(5/4)x4
indeterminate
∞
f'(x)=
limh→0(f(x+h)−f(x)h)\lim_{h\rightarrow0}\left(\frac{f\left(x+h\right)-f\left(x\right)}{h}\right)h→0lim(hf(x+h)−f(x))
limx→c(f(x)−f(c)x−c)\lim_{x\rightarrow c}\left(\frac{f\left(x\right)-f\left(c\right)}{x-c}\right)x→clim(x−cf(x)−f(c))
dydx\frac{\text{d}y}{\text{d}x}dxdy
an equation for the slope of the tangent line
limh→0(5(x+h)2−5x2h)\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)h→0lim(h5(x+h)2−5x2)
5x25x^25x2
10x10x10x
10
DNE
ddx[x3]\frac{\text{d}}{\text{d}x}\left[x^3\right]dxd[x3]
6x6x6x
3
3x23x^23x2
6
limx→2(x2−4x−2)\lim_{x\rightarrow2}\left(\frac{x^2-4}{x-2}\right)x→2lim(x−2x2−4)
2
4
8
limx→∞x2+3x−5\lim_{x\rightarrow\infty}x^2+3x-5x→∞limx2+3x−5
−∞-\infty−∞
0
∞\infty∞
limx→∞(x2+x−3x4−x3+1)\lim_{x\rightarrow\infty}\left(\frac{x^2+x-3}{x^4-x^3+1}\right)x→∞lim(x4−x3+1x2+x−3)
1
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