Use polar coordinates to evaluate: a) SSRdA/(x²+y²+1) where R is the region in the upper second quadrant between concentric circles (origin- centered) of radii 2 and 3. Sketch:

Q: T -2 -1 4 3 2 - -3 1 3. From the above graph of y = f(x), find the following limits: (a) lim f(x) =…

A: (a)  limx→-4f(x)=2   (b)  limx→-3f(x)=-2   (c)  limx→-2f(x)=-3   (d)  limx→1f(x)=infinite

Q: 67. = 2x − 7, y(2) = 0 dy dx dy 68. = 10 - x, y(0) = -1 dx 1 69. dx + x, x > 0; y(2) = 1

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: find differential equation of the following equation 3) dy +xsin(2y) = x cos² (y)

A: Given

Q: Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-…

A:

Q: 8. For what value of the constants A and B is the function f continuous on (-∞, ∞)? Ar + B for r 2

A: Please see the the answer below.

Q: sider the function p 3 of 3: Find lim f(x). x--6 f(x) = = lim f(x) x--6 Sx² + 12x + 22 19x + 100 if…

A: Topic:- limit and continuity

Q: Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-…

A: We need to choose correct option.

Q: Step 1 of 4: Find lim f(x). x--3- Enable Zoom/Pan 10 10 -10 Keypad Keyboard Shortcuts Selecting a…

A:

Q: Let f(x) be a function given by f(x) = (a) Prove whether f(x) is a Dirichlet function. (b) Find the…

A: Given

Q: A door is swung open by applying a 60 N force as shown, 2.0 m from the hinges. 2.0 m 100° 60 N ←--…

A: We have to find the torque applied at the hinge of the door.

Q: 5. If f(x) dx = 12 and f f(x) dx = 4, then all of the following must be tru a. ff(x) dx = 16 ✓ b.…

A: Given that∫25fxdx=12 and ∫58fxdx=4Solution :a.∫28fxdx=∫25fxdx+∫58fxdx                 =12+4…

Q: Let f(x, y) = 2x and C be the line segment on the plane from (0, 0) to (3, 4). Evaluate the line…

A:

Q: Let g(x)= log4 (13-5x). State the domain of g using set or interval notation. . State the range of g…

A: g(x)=log413-5x Given function g is unbounded when 13-5x=0⇒x=135 The equation of the vertical…

Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

A:

Q: 3. Evaluate 5 sin rdx B

A:

Q: Let F(x) = x √ √2+1 dt. Find F"(1) 3

A: Given: F(x)=∫3x t2+1dt Leibniz integral rule for differentiation states that ddx∫a(x)b(x)…

Q: Suppose 8 3n f(x) = n! (x - 7) n n=0 7 To determine So f(x) dx to within 0.0001, it will be…

A: We have to find the value of integral.

Q: 8 34) 2xe-x² dx <80 A) Convergent B) Divergent

A:

Q: Determine the equation of the hyperbola with center (-1, −6), a focus at (-1,-16), and a co-vertex…

A: I am attaching image so that you understand each and every step.

Q: Find the two values of k for which y(x) = ex is a solution of the differential equation y'' - 14y' +…

A: Solution is here

Q: 2. The graph of f(x) is shown to the right and has the following characteristics. 100 f(x) = x55x4 +…

A: We can solve this as follows:

Q: + [ƒ(2)₁ Suppose that fand gare continuous functions such that 1 [ g(x)dz -3, find f(x)dx= 2 and +…

A:

Q: Find the relation between backwards finite difference and average operator.

A: Given

Q: Find the vector equation of the plane that contains the line = [2,0,5] + t[2,-1,3] and passes…

A:

Q: Convert the Polar coordinate to the Cartesian coordinate. 1. r= 1+2r cose 2. r=1-cos8

A:

Q: Given plane z: 3x+2y+z-3=0, point P(1, -2, 3), and lines 1₁:an 4₂: (3, 6,-5)+(2, 3, 1), find: d) the…

A:

Q: Find the general antiderivative of f (x) = O2 ln ln 2x + C 1 O + C - 2 ln 2x O-In In 2x + C 1 O + C…

A: The function is given by fx = 4xlnx2 To evaluate: The most general antiderivative of the function.

Q: 12 Given that f(x) = 2x 3 + x - 3, evaluate the function f(-2). 11 -69 -21

A:

Q: The Kirk Kelly Kandy Company makes two kinds of candy, Kisses and Kreams. The profit, in dollars,…

A:

Q: The graphs of a quadratic function and a cubic function are shown below. Both graphs have integral…

A: Given problem:-

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y =…

A:

Q: y = ln x and x - y -4 = 0

A: Explanation of the answer is as follows

Q: Ju -To uv-s to Explain why the substitutions below are inappropriate. Let = x dx 1. Suppose we apply…

A:

Q: Solve the following second order differential equation, clearly showing all calculation steps d²y dy…

A:

Q: Determine the vector and cartesian equation of the plane that passes through the points A(−3, −2,0),…

A:

Q: E) Evaluate the triple integral on the left in each of the following: (a) ff₁dz dx dy = 1 "dz dy dx…

A:

Q: Find dy/dx of the following: a. y=sinh-5x b. y=sinh-e* c. y = cosh¹ √√x

A: To find dydx for the given y.

Q: x² + y² Briefly differentiate directional derivatives with suitable graph and equations.

A: This is a problem related to vector calculus. Based on the general formula and calculation we will…

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: Determine whether the improper integral is convergent or divergent. 33) S ∞ dx x2/5 0 A) Convergent…

A: We know that integration of xn   is xn+1/n+1.   Here i attached the solution of this question.

Q: Use linear approximation, i.e. the tangent line, to approximate √81.3 as follows: - Let f(x) √x.…

A:

Q: cost, y = sint, at the point where t 0 ≤t≤ 2π -O?! =

A:

Q: y 3. The region bounded by the curve y=sec x, the x axis, the axis and the line x=0.25pi is revolved…

A: The given curves are; y=secx, y=0 x-axis, x=0 y-axis, x=0.25π So, the bounded region is as shown…

Q: Use Leibnitz's Theorem to calculate the 4th derivative of y = x+sin(4x)

A:

Q: 1 2. Determine the numbers at which the vector-valued function R(t) = t²i+ ln (t-1)j + 1 ) ³ + + = =…

A:

Q: Find the first five non-zero terms of the Taylor series for f(x) = 1 3 Jo.[ + + + Written compactly,…

A: Use taylor series formula for the function

Q: 50° E 30° D In the figure above, line segment AC is tangent to the circle with center O at point B.…

A:

Q: 9- Solve the question. Lim cos(2x)/x хэл

A:

Q: Find and sketch the domain for f(x, y) = ² 2x-14y²

A:

Q: Find the average value gave of the function g on the given interval. TU TU g(x) = 6 cos(x), 2 2 gave…

A: We will find the average value of function as shown below