For the function h whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)The x y coordinate plane is given. The curve enters the window at the point (−5, 0), goes up and right to the open point (−3, 4), and goes down and right to the closed point (0, 1). The curve starts again at the open point (0, −1), goes up and right to the open point (2, 2), and then oscillates at an increasing rate between y = 2 and y = 4 until it reaches the x-value of 5. Between the x-values of 4.5 and 5 the oscillations are too close together to distinguish individual curves. At (5, 3) the oscillations stop and the curve goes up and right, changes direction at the approximate point (7, 4.8), goes down and right, and exits the window in the second quadrant.(a)lim x → −3− h(x)(b)lim x → −3+ h(x)(c)lim x → −3 h(x)(d)h(−3)(e)lim x → 0− h(x)(f)lim x → 0+ h(x)(g)lim x → 0 h(x)(h)h(0)(i)lim x → 2 h(x)(j)h(2)(k)lim x → 5+ h(x)(l)lim x → 5− h(x)

The graph of a function g is shown.The x y-coordinate plane is given. A function labeled y = g(x) with 4 parts is graphed.The first part is a curve, enters the window in the second quadrant, goes up and right becoming less steep, crosses the y-axis at approximately y = 2.5, and ends at the open point (2, 3).The second part is a curve begins again at the open point (2, 1), goes up and right becoming less steep, and ends at the open point (5, 2).The third part is the closed approximate point (5, 1.2).The fourth part is a curve, begins at the open point (5, 2) goes down and right becoming more steep, and exits the window in the first quadrant.Use it to state the values (if they exist) of the following:(a)  lim x → 2− g(x)(b)  lim x → 2+ g(x)(c)  lim x → 2 g(x)(d)  lim x → 5− g(x)(e)  lim x → 5+ g(x)(f)  lim x → 5 g(x)SolutionLooking at the graph we see that the values of g(x) approach as x approaches 2 from the left, but they approach as x approaches 2 from the right.Therefore (a) lim x → 2− g(x) =     and    (b) lim x → 2+ g(x) = .Since the left and right limits are different, we conclude that (c) the limit as x approaches 2 of g(x) does not exist.The graph also shows that (d) lim x → 5− g(x) =     and    (e) lim x → 5+ g(x) = .This time, the left and right limits are the same and so, by this theorem, we have (f) lim x → 5 g(x) = Despite this fact, notice that g(5) ≠ 2.

The graph of a function f is given in the figure.A curve is shown on the x y coordinate plane. It begins at the point (−2, −1), goes up and to the right, passes through the approximate point (−1, −0.2), and passes through the negative x-axis at the approximate point (−0.8, 0). It then continues up and right, passes through the positive y-axis at the point (0, 1), and reaches a high point at (1, 3). It then goes down and right, passes through the points (2, 2) and (3, 1), and ends at the approximate point (4, 0.5).(a)Find the value of f(1).(b)Estimate the value of f(−1).(c)For what values of x is f(x) = 1? (Enter your answers as a comma-separated list.) (d)Estimate the value of x such that f(x) = 0.x = (e)State the domain and range of f. (Enter your answers in interval notation.)domain range (f)On what interval is f increasing? (Enter your answer using interval notation.)

The graph of a function g is shown. The x y-coordinate plane is given. The curve begins at the point (−2, 0), goes up and right, passes through the point (−1.5, 1), goes up and right, changes direction at the point (−1, 1.5), goes down and right, passes through the point (−0.5, 1), goes down and right, passes through the origin, goes down and right, passes through the point (0.5, −1), goes down and right, changes direction at the point (1, −1.5), goes up and right, passes through the point (1.5, −0.5), goes up and right, changes direction at the point (2, 0.5), goes down and right, crosses the x-axis at x = 2.5, goes down and right, changes direction at the point (3, −1), goes up and right, passes through the point (3.5, −0.5), goes up and right, and ends at the point (4, 0.5). Estimate 4 −2 g(x) dx with six subintervals using the following. (a) right endpoints 0 Correct: Your answer is correct. (b) left endpoints -0.5 Correct: Your answer is correct. (c) midpoints

Graph the function.g(x) = 5 cos(x)The x y-coordinate plane is given. A curve has a cycle that repeats horizontally every 2𝜋.One cycle starts on the x-axis at x = −𝜋, goes up and right becoming less steep, changes direction at the point (−𝜋⁄2, 5), goes down and right becoming more steep, crosses the x-axis at x = 0, goes down and right becoming less steep, changes direction at the point (𝜋⁄2, −5), goes up and right becoming more steep, and stops on the x-axis at x = 𝜋.The next cycle starts at x = 𝜋. The x y-coordinate plane is given. A curve has a cycle that repeats horizontally every 2𝜋.One cycle starts on the x-axis at x = −𝜋, goes down and right becoming less steep, changes direction at the point (−𝜋⁄2, −5), goes up and right becoming more steep, crosses the x-axis at x = 0, goes up and right becoming less steep, changes direction at the point (𝜋⁄2, 5), goes down and right becoming more steep, and stops on the x-axis at x = 𝜋.The next cycle starts at x = 𝜋. The x y-coordinate plane is given. A curve has a cycle that repeats horizontally every 2𝜋.One cycle starts at the point (−𝜋, 5), goes down and right becoming more steep, crosses the x-axis at x = −𝜋⁄2, goes down and right becoming less steep, crosses the y-axis at y = −5, goes up and right becoming more steep, crosses the x-axis at x = 𝜋⁄2, goes up and right becoming less steep, and stops at the point (𝜋, 5).The next cycle starts at x = 𝜋. The x y-coordinate plane is given. A curve has a cycle that repeats horizontally every 2𝜋.One cycle starts at the point (−𝜋, −5), goes up and right becoming more steep, crosses the x-axis at x = −𝜋⁄2, goes up and right becoming less steep, crosses the y-axis at y = 5, goes down and right becoming more steep, crosses the x-axis at x = 𝜋⁄2, goes down and right becoming less steep, and stops at the point (𝜋, −5).The next cycle starts at x = 𝜋.State the domain and range. (Enter your answers using interval notation.)domain range

Use the graph to state the absolute and local maximum and minimum values of the function. (Assume each point lies on the gridlines. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)A function with two curves, three closed points, and three open points is graphed on the x y coordinate plane. The first curve begins at the closed point (0, 2) increases to the open point (1, 4) decreases to (2, 2) increases to (4, 5) decreases to (5, 3) then turns sharply and increases to the closed point (6, 4). The second curve begins at the open point (6, 3) and decreases to the open point (7, 1). The closed point (1, 3) is graphed.absolute maximum value 5 absolute minimum value 2 local maximum value(s) 5 local minimum value(s) 2,3