Evaluate: (x^2-1)/(x-1) if x goes to 1?

Mathematics

1 answer:

egoroff_w [7]3 years ago

6 0

Step-by-step explanation:

$\displaystyle \lim_{x \to 1} \dfrac{(x^2 - 1)}{(x-1)} = \lim_{x \to 1} \dfrac{(x - 1)(x+1)}{(x-1)}$

$\:\:\:\:\:\:\:\:\displaystyle = \lim_{x \to 1} (x+1) =2$

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g For the curve parameterized by x(t) = 3 sin t, y(t) = 5 cost, for −π/4 ≤ t ≤ π/2: (a) Sketch the curve and the direction trace

tamaranim1 [39]

Answer:

a) See the file below, b) $s = \int\limits^{0.5\pi}_{-0.25\pi} {[\left( 3\cdot \cos t\right)^{2}+\left(-5\cdot \sin t \right)^{2}]} \, dx$ , c) $s \approx 9.715$

Step-by-step explanation:

a) Points moves clockwise as t increases. See the curve in the file attached below. The parametric equations describe an ellipse.

b) The arc length formula is:

$s = \int\limits^{0.5\pi}_{-0.25\pi} {[\left( 3\cdot \cos t\right)^{2}+\left(-5\cdot \sin t \right)^{2}]} \, dx$

c) The perimeter of that arc is approximately:

$s \approx (\frac{1}{4} + \frac{1}{8})\cdot 2 \pi\cdot \sqrt{\frac{3^{2}+5^{2}}{2} }$

$s \approx 9.715$

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3 years ago

1-116 1.2.6

ankoles [38]

Answer:

A. 30 adults; B. 24 not dolls

Step-by-step explanation:

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If five-eighths of the prizes were dolls, then three-eighths of the prizes were not dolls.

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