□ 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: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

A:

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: How long will it take to drive 700 km at 100 km per hour, if you take a 1-hour break after every 5…

A: We have to find time taken to drive 700km using given data. We will use formulaes,…

Q: x=3 Qs. A: Find * x²dx by using Riemann integral.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Express lim i odinflabai bas esinlob otatlavo noo T nousitedura oidd grian olderolm i=1 sin r;Ar as…

A: Answer: the evaluation of above integral is as shown below:

Q: Please show all steps

A:

Q: Let f [0, 6] → R be the function defined as : f(x) = = -2, [4/x], if 0 < x < 1, if 1 ≤ x ≤ 6. Show…

A: Result :Every bounded function f  : [a, b] → R having atmost a finite number of discontinuities is…

Q: If m(E) = 0, show that any function f: E → Ris Lebesgue integrable and Se f = 0.

A: Given, mE=0 So, a measurable function f:E→ℝ is said to be Lebesgue integrable  (or simply inferable)…

Q: (a) Let f: R" → R be a function given by f(x₁, 2,...,xn) = x²₁₁x²2x², where n = 1. Show that the…

A:

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: defined function g(x) [₁] g: sin² x, → as if x E Q 0, others a. Determine the Upper Riemann Integral…

A: Definition:

Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. (a) (b) (c)…

A: Evaluation of integral

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