The piecewise function h(x) is shown on the graph. What is the value of h(2)? −2 −1 0 3

2 answers:

9 0

Answer:

C..............................

5 0

We need to find the value of h(2).

h(2) represents the value of h function for x=2.

We need to check the value of function on the graph where h is 2.

From the graph, we can see for x=2, we have a solid dot for y coordinate at 0 and a hollow dot at y coordinate at 3.

Because hollow dot represents excluded value.

Therefore, we would take y coordinate of solid dot of the graph at x=2.

Therefore, f(2) = 0.

<h3>Correct option is third option, that is 0.</h3>

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General Formulas and Concepts:

Calculus

Differentiation

Basic Power Rule:

Parametric Differentiation

Integration

Arc Length Formula [Parametric]: $\displaystyle AL = \int\limits^b_a {\sqrt{[x'(t)]^2 + [y(t)]^2}} \, dx$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \left \{ {{x = t - cos(t)} \atop {y = 1 - sin(t)}} \right.$

Interval [0, π]

Step 2: Find Arc Length

[Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]: $\displaystyle \left \{ {{x' = 1 + sin(t)} \atop {y' = -cos(t)}} \right.$
Substitute in variables [Arc Length Formula - Parametric]: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{[1 + sin(t)]^2 + [-cos(t)]^2}} \, dx$
[Integrand] Simplify: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx$
[Integral] Evaluate: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}$