Example -3 .2 Evaluate I (x+ 2y – z) dx dy dz I (x + 2y – z) dx dy dz - 2 SLE + 2xy – xz dy dz - 2 (2 + 4y – 2z) dy dz %3D - = [ 12y + 2y² – 2yz", dz - 2yz]", dz (2 +2 – 2z) – (–2+ 2+2z) }dz %3D (4 – 4z) dz 3 4z – 2z? (12 – 18) – (4 –- 2) = -8 %3D Detailed explanation, .understand this is an example

Q: d) (i) Use the alternating series test to show that the series converges. k+1 k +3 Σ-) k(k+1) k=1

A: To show that the given series converges using alternating test.

Q: :(7e*) cos (4e") dx Evaluate: e cos --cos (3e*) – cos (1le*) + C 22 ® os (3e*) +cos (11e)+c COS 6.…

A: We have to find value of given indefinite integral

Q: Evaluate (s 2'ds Oa 2 1) In2 Ob. 2 (sln2 - 1) (In2)2 O. 2(sin2 - 1) (In2)2 Od 2° +1) In2

A:

Q: Q1: Find the integration of : (choose 3 only ) 1. Sc (3 sin x)cos (4 sin x). cosxdx Cos

A:

Q: Find the derivative of f(x)= (In x O a. 6x(In x) O b. 24(In xỷ c. 24 In x O d. 12(In x)

A:

Q: 25s^2+202s+25. FACTOR THIS QUADRATIC EQUATION ACCURATELY.

A: 25s2+202s+25=0We know that solution of quadratics equation ax2+bx+c=0 is x=-b±b2-4ac2a Herea=25,…

Q: Find the general solution of (2x – y) dy = 2y – x - da

A:

Q: Q2) Convert the polar function r tan20 to cartesian.

A:

Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) *+ 2y = 3 ,y (0) =…

A:

Q: Evaluate f Vr+ V?dx Oa. 3 am +2) +C (V2) +C can) Ob. 2 am +2) +C 30 om +C (25) Oc 2 an +m) +C O d. 5

A:

Q: Q2) Solve the D.E xy(x? + 1)dy - (y? + 1)dx = 0 %3D

A:

Q: Show that the set of all points P that are twice as far from (-1,5,3) as from (6,2, –2) is a sphere.…

A: The set of all points P that are  twice as far from -1, 5, 3 as from 6, 2, -2. Let coordinate of a…

Q: 1. Mang Vicente has 1000m of fencing material and wishes to enclose a rectangular field. Two (2)…

A: Mang Vicente has 1000 m of fencing material and wishes to enclose a recangular field. Two adjacent…

Q: 36. (х, у) —- (0, 0) lim (x + y²) In(x² + y²)

A:

Q: Apply the chain rule to differentiate the following functions. Show your complete solutions and…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: to this answer. Evaluate the left-hand limit of as f (x) = x8. 16-2x O 1/2 O -1/2 O undefined

A:

Q: Question 18 Consider Evaluate O (9x4+6x)e (x3+y2) O (3x²+6x)e «³+y?) O (6x²+ 3x)e «³+y?) O (6r*+9x)e…

A: Topic = Derivative

Q: Find the equation of the tangent line and normal line to the curve ? = √? − 3 and whose normal line…

A:

Q: Cha invests Php5,000 in an investment that earns 6% per annum. How many complete years does it take…

A: Given Cha invested(P)= Php5,000Rate of interest (R)=0.06Time (t)=?Amount (A)=Php 10,000We know that…

Q: Evaluate: | sech[In cosx]tanx dx A -2 tan -1(e cosx) +C В -2 tan -1(cosx) +C 2 tan -(ecosx) + C (D 2…

A:

Q: F'(x) = (ax3 + b)2 O none of the choices O 1 За ах3 + b 1 1 2a ax3 + b 1 1 - За аx3 + b. o 1 2a (…

A:

Q: Question 5. Find the Laplace transform of the following function by using the integral definition of…

A: Given problem:-

Q: Find the value of A which is defined as the angle between i+j and j+ k.

A:

Q: : Se' com (7e')cos (4e")de Evaluate: (A) -cos (3e") –cos (11e*) +C 22 -cos (3e*) + -cos (11e*) +C B…

A:

Q: Evaluate the following integral using Partial Fractions Method: x³ + x? y = dx х2 + х — 2 -

A: Follow the procedure given below.

Q: Let f(x) be the function 11a - 5x+4. Then the quotient f(8 + h) - f(8) can be simplified to ah + b…

A:

Q: Let C be the line segment connecting the point p = (2,5, 0) to the point q = (0,6, –5). Find a curve…

A:

Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

A:

Q: 1. The graph of a function y = a/b(x-h)+k shown below. -1 -40 Algebralcally determine two different…

A:

Q: Find h'(x) if h(x) = x³e*sin x. O a. h'(x) = 3xe*sin x + x'e*sin x + x'e*cos x 3X, O b.h'(x) =…

A:

Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2 ,y = 4.

A: Set up the triple integral and solve to get the desired volume.

Q: 22 – 9x? = 1 4.

A:

Q: Q4) Evaluate the following integral using Trigonometric Substitutions Method: 2 y = - x dx

A:

Q: Evaluate the definite integrals

A:

Q: Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until twO…

A: Let's find.

Q: Let a = 2i – 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8…

A: Here we have to find the dot product.

Q: Which series converge in the interval described by |x| < 1? 1. 1+x+x^2+... 2. x+x^3 + x^5+... a.…

A:

Q: Type your answers in the following order and format: a=1,b=2. DO NOT include spaces in between…

A:

Q: (x – y)dr + xdy = 0.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Determine the area of the circle whose center is at the origin and tangent to the parabola y = x2 -…

A: y=x2-100from the grapph attached, Parabola cuts X-axis at (10,0) and (-10,0)

Q: Determine an antiderivative, y, of the given derivative, y. Then use the given condition on y to…

A:

Q: Question 4 -e-*) dx Evaluate: A '+C 2 B cosh x +C sinh x +C D – sinh x +C E None (F -cosh x +C 2

A:

Q: Find f"(-1) if Ax) = (x). -6 O -5 O 5

A:

Q: Evaluate: / yº sech(eThy ) tanh (e "hy ) dy 7Iny -mch(v^) + C None -ech"(,?) + C

A:

Q: 6.Find all the first partial derivatives of each function x² – y² c. f(x,y) ху с. = d. f(x,y)=e* cos…

A:

Q: Solve the D.E dy – (2x/1- y2)dx = 0

A:

Q: Find f"(1) if Ax) = X+1. %3D 1 1 1/4 12 OOO

A: To find f'1 if fx=xx+1.

Q: 4 r4-y Evaluate triple integral , S S dz dy dx -2

A: We have to evaluate the triple integral  ∫-22∫x24∫04-ydz dy dx.

Q: Consider the solid bounded by the planes: =x+y, z=30, x=0, y=0. Determine the volume of the solid.

A:

Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.