1. Evaluate [F.dr where F=xz²i+yj-x²k along the curve x = sin cos0, y = sin²0, z =cose with increasing from 0 to π/2. (a) (c) 1310910 (b) (d) 7 10 11 10

Q: Let f(x) = -2 ln(cos(x)) f''(x) =

A: dlnxdx=1xdcosxdx=-sinxdtanxdx=sec2xsinx cosx=tanx

Q: f (x) = 3 sin x + 3 cos x, [0, 27]

A: Consider the function: fx=3sinx+3cosx Differentiate the given function with respect to “x” then,…

Q: d dx d du d dz d [12 cos ¹2x] dy d dq [4 sec ¹3u] [10 tan-¹2z] [6 csc-¹4y] [9 cot-¹39]

A:

Q: . Does the function cos x x + 0 f(x) = 0, x = 0 have a derivative at x = 0? Explain.

A: Consider the given function fx=1-cosxx        x is not equal to 0x=0

Q: The Bay of Fundy in Canada has the largest tides in the world. The difference between low and high…

A: Given, Difference between low and high water level = 18 m  y = D + A cos (B(t - C))

Q: 1. þompute and simplify the derivative with respect to x for each of the following functions: a)…

A:

Q: 1. Find each derivative. a) y = sin- X c) f(x) = ln- sin x COS X b) y = cos(x² - 2x-8)

A:

Q: Differentiate. f(0) = 0 cos(0) sin(0) f'(0) =

A:

Q: 1. Differentiate. Do not simplify. а. f(0) = 3cos(0*)sin(0³ – 2) b. f(x) = 4x + 25-x² + 2x-1

A:

Q: Find the equation of the tangent line T to the graph of f(x) = 8 sinx at the given point (6,8 sin…

A: given  f(x)=8sinx d dx(sinx)=cosxstandard form of quation is y-y1=m(x-x1)where m is slope m=f'(x)