Consider the function f: R → R define by f(x) = a?x3 + x² with a a real constant , a + 0, We can affirm that the maximum relative of and the minimum relative of f can be reached when: O a) z y x= 0 3a2 Ob) z 2 ya=0 3a2 2 Oc) z = 0y z= 3a2 -2 O d) x = 0 y x = 3a2

Q: Question 2 Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2…

A:

Q: Find the area of the region bounded by the graphs of f (x) = x³ and g (x) = x. (A) 1 c) 0.5 3.

A:

Q: Find the volume of the solid that results when the shaded region is 8 revolved about the indicated…

A: Volume of revolution

Q: sider the scalar function: f(x, y) = sin(3x)ey I the gradient: Vf(x, y) I the Laplacian: v2 f(x,y)…

A:

Q: 1 -dt , find g'(2). V4 +t5 If g(x) =

A: Let's find.

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. da dz dy = y -54 J-36 %3D

A:

Q: Show that ā b 12

A:

Q: Find the area of the region that is enclosed by the cardiod r = 12 + 12 sin 0.

A: form a integral then solve

Q: Find the arc length of the parametric curve. x = 24 cos(t), y = 24 sin(t), z = 7t; 0<t< T L

A:

Q: Use a double integral to find the volume under the plane z=38x+y and over the rectangle…

A: We have to find the volume using double integration.

Q: 8 cossa da V sin a

A: Integral

Q: xydA R

A:

Q: Skatch the curve in polar coordinates. r=I+ 3sino 2 -6 -4 -4

A: Given curve r= 1+ 3sin( theta)

Q: A property has been mapped, and the height above sea level is determined to be represented by the…

A: Given a scalar field representative of height.

Q: Evaluate the double integral. /| 4x²sin y²dA; Ris the region that is bounded by y = x², y = -x², and…

A: Given problem:-

Q: Evaluate the integral. n/2 5 cos?0 de

A:

Q: c. lim G)3-* - 1 X-3 2

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 4…

A:

Q: 5. Find a Taylor series expansion around x = 1 for f(x) = 6. Without solving the exact answer,…

A: 5) The Taylor series formula around x=1 is:…

Q: Question * Determine the nature of convergence of the following improper integrals 00 1 dx 1+ x* A =…

A: ∫a∞f(x)dx=limR→∞∫aRf(x)dx  If the limit exists and is a finite number, we say the improper integral…

Q: Use double integration to find the volume of the solid bounded by the paraboloid Z = 9x + y, below…

A:

Q: dx 2 X + 4

A: Topic = Integration

Q: Determine which value best approximates the area of the region bounded by the graphs of f and g.…

A:

Q: 1- Show that the following subset is a subgroup. H = {o e S, lo(n) = n}cS,

A: Explanation of the answer is as follows

Q: Find the volume of the solid that results when the region enclosed by the given curves is resolved…

A: Solution is done in step 2

Q: In sketching the graph of y=f(x) = 2sin -5, we translate the graph of y=2sin by 5 units downward and…

A: To translate the given function.

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

A: Given; y=x^2 between x=1 to x=2

Q: A businessman borrowed Php2,500,000 for 5 years at 5.5% simple interest. What amount must he pay at…

A:

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating d dt dt the product directly…

A: r1(t)=cost i+sint j +3t kdr1dt=-sint i+ cost j+3 kr2(t)=2i +t kdr2dt=k

Q: Consider the following planes. 5x + 2y – z =22 X- 4y + 2z = 0 (a) Find the angle between the two…

A:

Q: d. Calculate ri(t) · r»(t)] and d Edit dt [r1(t) x r2(t)] first by differentiating dt the product…

A:

Q: Evaluate the definite integral. 14t i + e*j+t k)dt (el4 – 1) i – (e-1 – 1) j + k 1-(6" -1) + i- (e~-…

A:

Q: Find the following for the given equation. r(t) = (e, 5t?, 6 tan(t)) (a) r'(t) = (b) r"(t) = (c)…

A:

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

A:

Q: 13.3 PARTIAL DERIVATIVES 29-32 Evaluate the indicated partial derivatives. I 29. f(x, y) = 9 – x² –…

A:

Q: Solve y" +3y'+2y =

A:

Q: True or False, and give a short reason: (a) If a function is differentiable, then it is continuous.…

A: Given problem:- True or False, and give a short reason:   (a) If a function is differentiable, then…

Q: The graph of a function y f(z) is shown. C. At which point IS the following true (Only type the…

A:

Q: Sketch the region R of integration and switch the order of integration. F(x, y) dy dx y 2 2 -4 -2 2…

A:

Q: Verify Green's Theorem by evaluating both integrals v? dx + x2 dy dA ax for the given path. C:…

A: 9

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: Evaluate the double integral. 7x*sin y²dA; Ris the region that is bounded by y = x³, y = -x³, and y…

A: double integral

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: Given

Q: Use a double integral to find the volume of the indicated solid. 9. z = 9-2 y 2. y=2 4 X=4

A:

Q: Evaluate the iterated integral. yz dx dz dy 45 в) 34 47/3 D) 5

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: Find the limit (if it exists). (If an answer does not exist, enter DNE.) 6t + sin(8t) i + e-4°k lim…

A: To find the limit of the given vector function.

Q: r = V cos 20 r = 5 cos 0

A:

Q: Consider the following algebraic functions. y = 1/x2 y = 0 x = 2 X = 7 Sketch the region bounded by…

A: Given :   y=1/x2 y=0 x=2 x=7

Q: 324-y' y dx dy 18

A: