Where is each function continuous? (b) f(z) = sin (1-r) I+3 (c) f(r)= In (d) f(r) = 12+5r +6

Q: Let R be the region shown in the accompanying figure. Fill in the missing limits of integration. y =…

A: Let's find.

Q: Find the average value of f(x) 1 -x + 5 over the interval 0, 4. fave

A:

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: We need to evaluate integral using Green's theorem.

Q: ||r(t) × r"(t)|| Use the formula k(t) to find «(t). 3 r(t) = e%i+ ej %3D K(t)

A:

Q: 3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

A:

Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

A: fx is differentiable and invertible function so that f(3)=4 and f'(3)=12

Q: 17-22 Use appropriate forms of the chain rule to find əz/du and əz/əv. I 17. z 3D 8x*у - 2х + 3у; х…

A:

Q: Find the directional derivative of f at P in the direction of a. f(x, y) = 17 tan ; P(-18,18); а—…

A:

Q: dx dy =

A:

Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

A:

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. V64-22 xy dy dx dz

A: Given: I=∫08∫064-z2∫0xxydydxdz   The Power rule: ∫xndx=xn+1n+1+C

Q: Two parallel sides of a rectangle are lengthened at a rate of 3 cm/sec, while the other sides are…

A:

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A:

Q: Find T(t) and N(t) at the given point. r(t) = 3 cos(t)i + 3 sin(t)j + tk; t = T .2. NG) = .2

A:

Q: Find the arc length L of the graph of r(t). 1 .3 r(t) = i+t j+¬V61² k, 2 <153 L =

A: Solve the following

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A:

Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows

Q: _ア-1 x² - 1' y(2) = 2 dx

A:

Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

A:

Q: Find the centroid of the region. NOTE: Enter the exact answers. (ï, §) = (?, ?) y = r

A:

Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

A: Solution:

Q: If f is differentiable at a number, x, then f is continuous at x.

A:

Q: find Fourier series on [0,2n] オーズ 0<x<T (12) f(x) = Tくx<2元

A:

Q: test the converg ence and divergence 27-1 2. (2h-1):

A:

Q: 12 9.

A: Use Trigonometric ratios

Q: Current Attempt in Progress Sketch the curve by eliminating the parameter, and indicate the…

A:

Q: Verify Green's Theorem by evaluating both integrals ам | y2 dx + x2 dy dA ду for the given path. C:…

A: Solution is given below:

Q: Find equation of the line if: A. Slope is 3/4 and through the point intersection of y-2x-5=0 and…

A:

Q: Consider the function g: IR → R , g(x) = 3x* – 32x2, the function has a turning point (x,y) for: 4 O…

A:

Q: Consider the expression: ey = 4x + y* , In which y is an implicit function of x , after derivation…

A: Given problem :- ey =4x+y4 , find y'

Q: Find the Laplace transform of: f (t) = v1+ sin t + (7t)14 + t² sin 2t

A:

Q: Consider the equation y"+ay'+by=f(x) where a and b are real constants. If the general solution of…

A:

Q: Consider the following. f(x) = x* – 4x² g(x) = x² - 4 (a) Use a graphing utility to graph the region…

A:

Q: Question 20 Evaluate JJ xy dA , where R is the region in y = x? R (A) 13/7 (в) 16/3 18 D) 20 2.

A: We have to find the area.

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. e…

A:

Q: Find the directed distance from the given line to the given point. (-1, 6) (5, 4) (10, 8) (1, 2)…

A:

Q: The intelligence quotient, or IQ, is a measure someone ability to reason and solve problems (some…

A: This question can be solved using the concept of normal distribution.

Q: Find the area bounded byf(x)=x^2-4x-5andy=x+1

A:

Q: In exercises 9–14, find all critical numbers and use the Second Derivative Test to determine all…

A:

Q: Use a triple integral to find the volume of the given solid. The solid bounded by the parabolic…

A:

Q: Find the four​ second-order partial derivatives for​ f(x, ​y)= 7x4y8 + 8x7y5 Fxx= Fyy= Fxy= Fyx=

A:

Q: Example 6 Video Example 0 A particle moves along a line so that its velocity at time t is v(t) = t2…

A: Given;  v(t)=t2-t-12.

Q: Evaluate the iterated integral. 1 2r y 8ry: dz dy dx

A:

Q: Find dy dx 21) tan y = eX + In 4x eX + 4 A) - sin² y хeх + 4 B) - xcot y

A: Given;  tany=ex+ln(4x).

Q: Prove that f : [−4,2] → R defined by f(x) = 7/x+5 is uniformly continuous on the interval [−4, 2]…

A:

Q: Find T(t) and N(t) at the given point. = e' cos t, y = e' sin t, z = e'; t= 0

A:

Q: Two functions are defined by f: x ax + I andg:x 4b **1, where a and b are constants. Given that f(a)…

A:

Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = V x2 + y2,…

A:

Q: Use a double integral to find the volume of the region under the graph of f(x, y) = xy and above the…

A:

Q: for the following differential equation (assume zero initial conditions), write the state variables…

A: Solution: Given