Find Value of that fulfills Intermediate Value theorem for integral fw = sinx t cosy ,...
Use the Mean Value Theorem to show that |sinx − siny| ≤ |x − y| for all x, y ∈ R.
Problem 3. Evaluate the integral co sinx dx. Hint: Apply residue theorem to the function f(z) = and the contour y of the following shape:
QUESTION 17 Find the integral. - sin x cos xdx - sinox +C 6 - sinx 5 + sin 5x 5 +C sinx -C
tion 5 sinx Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function h(x) 3int dt h'(x) = 3 cos(x)In(sinx) - h'(x) = 3 in (cos(x)s in(x))+ 1m3) - h'(x)=3\n(sin(x)cos(x)) - 31nYX h'(x) - 3sin(x) 31n(7) cosx 2 n'(x) = () - 3cos(x) 3inx sinx x h"(x) = 3sin(x)in(cosx) + 3inky 2x
4. Compute Fourier integral representation for f(x) = S\sinx[xST [x] > T = {leine $ " cosas # 1 (cos") ds = TT and deduce that 2:
Use the intermediate value theorem to show that the polynomial function has a zero in the given interval. f(x) = 2x® + 3x2 – 2x+8; (-8, -2] Find the value of f(-8). f(-8)= (Simplify your answer.) Find the value of f(-2). f(-2)= (Simplify your answer.) According to the intermediate value theorem, does f have a zero in the given interval? Yes Νο Ο
Theorem 20.8 (The Mean Value Theorem for Integral Calculus). Let f a, bR be continuous, and g a, bR be integrable and nonnegative. Then, there exists acE (a,b) such that (20.3) f(x)g(a)dx - f(c g(x)dr (ii). Apply Theorem 20.8 to show that 1 100 32 Jo (1 +r2)5
Theorem 20.8 (The Mean Value Theorem for Integral Calculus). Let f a, bR be continuous, and g a, bR be integrable and nonnegative. Then, there exists acE (a,b) such that (20.3) f(x)g(a)dx...
Verify Stokes's Theorem by evaluating F-T ds = For as a line integral and as a double integral F(x, y, z) - (-y+z)i + (x - 2)j + (x - y)k S: Z - 16 - x2 - y220 line integral double Integral I Need Help? Read it Watch Talk to a Tutor
Evaluate the line integral in Stokes Theorem to evaluate the surface integral J J(VxF)-n ds. Assume that n points in an upward direction F (xty,y z,z+x) S is the tilted disk enclosed by r()-(3 cost,4sint,7 cos t Rewrite the surface integral as a line integral. Use increasing limits of integration. dt (Type exact answers, using π as needed.) Find the value of the surface integral. JÍs×F).nds-ロ (Type an exact answer, using π as needed.)
Evaluate the line integral in Stokes...
Determine whether the integral is convergent or divergent Find the value of the integral (if it converges) and assign the value of 0 to the integral (if it diverges) Answer: άκ Determine whether the integral is convergent or divergent: x-4x+3 Find the value of the integral if it converges) and assign the value of0 to the integral (if it diverges). Answer Determine whether the integral is convergent or divergent: Find the value of the integral (if it converges) and assign...