For the function f(x) = 1 4 ex + e−x, prove that the arc length on any interval has the same value as the area under the curve. f(x) = 1 4 ex + e−x ⇒ f '(x) = ⇒ 1 + [f '(x)]2 = 1 + = 2 = [f(x)]2 The arc length of the curve y = f(x) on the interval [a, b] is L = b a 1 + [f '(x)]2 dx = b a [f(x)]2 dx = b a f(x) dx, which is the area under the curve y = f(x) on the interval [a, b].

ce pula mea vrei ma

step-by-step explanation:

gayule

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.