□ Use the definition of integral to prove that for = f'/h 1/x if X FO (x) is NOT if x=0 Riemann integral ble [0, 1]. (Hint: 200 £is divergent.)

Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

A: We have plotted the contour C: |z|=3 and the poles of the function f(z)=z-1z2z-8i-7 on the same…

Q: Please show all steps

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Q: ¡CON(I) 1 G(r): = -T₁₂ -2 dy 1-y³

A: Gx=∫x-2cosx11-y3dy To Find: Evaluate the above definite integral Using the Fundamental Theorem of…

Q: Answer: If f is continuous and [10 *f(t) dt = 12, find the integral [*²1² ƒ (1³) di dt.

A:

Q: Use integration by parts to evaluate lim Sest f(1)dt. (Let u = Z→∞J f(t) and dv = est dt.)

A: As per the question we are given a limit of an integral, and we have to use the integration by parts…

Q: f(x)dx =F(b)- F(a) Please explein in detar L, . To evaluate the integral, first find F(s).) How to…

A: Given  f(s) = 1+ s-3/2 We have to its definite integral  So first calculate it's indefinite integral…

Q: Use the Fundamental Theorem of Calculus to evaluate (if it exists) where If the integral does not…

A: Solution

Q: If the given three vectors are coplanar, then find the value of x. A = i-2j + 3k, B = xj + 3k, C =…

A: A, B, C are coplanar.So