EXAMPLE 4 Find the arc length for the curve y = 2x2 In(x) taking Po(1, 2) as the starting point. 16 If f(x) = 2x2 - In(x), then 16 SOLUTION f'(x) 1 + [F'(x)]? = 1 + = 1 + 16x2 0.5 + = 16x2 + 0.5 + 2 (1 + [F'(x)]² Thus the arc length is given by s(x) V1 + [f'(t)]²? dt dt %3D For instance, the arc length along the curve from (1, 2) to (4, f(4)) is 1 s(4) = + In(4) – 2 16 In(4) + 16 (rounded to four decimal places).

Q: 6. Find y' if y = ecotx? A. -2x [csc²(x²)] (ecotx") B. -[ csc (x*)] (ecotx") C. [cot(x²)]…

A:

Q: To plot points in polar coordinates, we use a grid consisting of ________ centered at the pole and…

A: A rectangular grid is useful to plot points in rectangular coordinates. A grid consisting of circles…

Q: Find the equation of the tangent line of f(x) = 8/x+3 at the point (4, 19) . Express your answer in…

A: Find the equation of the tangent line of fx=8x+3 at the pint (4,19).

Q: Suppose f(x) = 4(x - 9)-¹/2. (a) Find f'(x). f'(x) = X X # (b) Find an equation for the line tangent…

A:

Q: Find f'(x). f(x) = (3x° + 6) ª f'(x) =|

A: ddx((3x6+6)4) Apply power rule: (u(x)n)'=u(x)n-1*u(x)=4(3x6+6)3*ddx(3x6+6)

Q: (a) y = 3x-1 (b) x² + y² = 1 (c) y = sin(x)

A:

Q: Suppose f(x) and f'(x) have the following values. -5 -4 -3 -2 -1 f(x) 8 10 15 16 14 f'(x) -2 -3 9 -5…

A: We need to find  out h'(-5).

Q: if f(x)=6x^2 - 4x, find f'(2) and use it to find the equation of the tangent line to the parabola…

A:

Q: Suppose f(x) and f'(x) have the following values. -1 0 12 8 -5 10-2 8 -6 -5 7 f(x) f'(x) -2 0 -3 Let…

A: The given table is:

Q: The tangent line to the graph of y = g(x) at the point (6, 7) passes through the point (8, 0). Find…

A:

Q: Find an equation of the tangent line to the graph of y=9* at the point (-1,9). 01) y=9_(x+1) 9 9 ○…

A: