Use Cartesian coordinates to evaluate Jff v² av . D where D is the tetrahedron in the first octant bounded by the coordinate planes and the plane 2x + 3y + z = 6. Use dV= dz dy dr. Draw the solid D.

Q: 2. Solve for x. 45x-x² = 4-6 a. b. (1 − x)5 = (2x − 1)5 - 60 c. 55 = 1+5e-0.6x d. 3 log x + 10 =…

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Q: Q4: Solve the following integration corrected to 3 decimal places using: 1. Trapezoidal rule 4…

A: The given integral is 4/sqrt(x), limit from 1 to 5.

Q: Let L(y)=(x-1)y" - xy + y a) with the observation that y, zx is a solution of L(4)=0 on (1,00), by…

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Q: 7. Compute the area of the region R enclosed by the curves y = x² - 1 and y = 1- x.

A: We have to find out the area

Q: Find the first three nonzero terms of the Taylor expansion for the given function and given value of…

A: The given function is 3tanx, a=7pi/4.

Q: 3(a) The cost of manufacturing motor cycles (per day) is related to number to number of motor cycles…

A: Here we have to use the concept of derivatives.

Q: 1. Find the distance between p(-2, 3,0) and Q(2,1,5). 2. Find the direction of A = 2i - 3j+7k. 3.…

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Q: Evaluate the double integral: S² SATI 1/3 x² +1 (Hint: Change the order of integration to dy dr.) dr…

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Q: Does the following series converge or diverge? 4√n Σ 3/2 10n +7n+7 n=1 O The series diverges. The…

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Q: Evaluate the double integral that will find the volume of a solid bounded by 2=1-2y²-3r² and the ry-…

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Q: cos(x) 2x+3

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Q: 7. The value of sin(1¹/3) dt 12/3 S

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Q: Q5/ Solve for x the following inequality and show their solution set (x: x2-x-300)

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Q: (d) lim 1-x-x² x-∞ 2x³ - 3x + 1

A: In this question, we want to evaluate the limit of the given expression.

Q: I. Simplify. Write "undefined" for expressions that are undefined. -1 5 -3 6 3 3.) 5 0

A: We have to find out product

Q: Q3: A) Find the limits below x² + sin²y 1) lim (x,y)-(0,0) 2x² + y² 2) (x, lim y)-(1,1) x+y x² - 2xy…

A: Concept: Here we have given multivariable limits  To find its limit first use direct substitution…

Q: 2 S Sec'x In cotx) dx (

A: We will solve the problem.

Q: / If y" + 2y' F5y = e-Sint, y(0) = 0, y' (0) = 1

A: We solve the given differential equation using the higher order LDE techniques.

Q: (2) Z/(5) =........ (i) (5) (ii) 5Z (iii) {[0],[1],[2],[3],[4]}

A: We have to find out integer

Q: Function f is graphed. -4 -3 -2 A Y 4 3 2 t 1 1 4 2 3 -1+ -2- -3- -4 Find f (2) da. Give an exact…

A: We can find the given integral by using the application of the integral.

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

A: Let's solve given diffrential equation by using laplace transform.

Q: 2. Given the values for f(x) on the table, approximate the area under the graph of f(x) from x = -5…

A: Let's find approximate area under the graph.

Q: Find the area of the region above the curve y=x²-6, below y=x, and above y=-x.

A: Let's find area of region.

Q: 2 -1 4 4 -6 1 -3 -5 北

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Q: Function h is graphed. h -4 -3 -2 L y 4 3+ 2- 1 -1- -2+ -3- 12 3 4 Find h(2) da. Give an exact…

A: This question can be solved using the concept of area under curve.

Q: INSTRUCTIONS: Please write clearly and understandable way. • Write all the corresponding Given with…

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Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

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Q: - show that (x, y, z) = 8²4 PDE : 2²4 дуг дуг + + x² + y² + z² = 0 8²4 dz² satisfies the

A: Given that ϕ=1x2+y2+z2

Q: Determine the exact length of the polar curve r 3 sin for 0≤0 ≤T. =

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Q: 2. Express the iterated integral as a double integral in polar coordinates. 1 X 1 Lo dy dx 16/2 x² +…

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Q: Find the area of the region enclosed by the curves y =

A: answer is in next  step

Q: 3) Locate the bifurcation values for the one parameter family and draw phase lines for values of the…

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Q: I. A delivery rider is travelling along a horizontal line such that its directed distance from his…

A: This is a problem related to derivative of the distance function. Based on the general formula and…

Q: Solve the given differential equation. All solutions should be found. (5y¹ + 2x³y) dx − (4xy³ + x¹)…

A: Simplifying (5y4 + 2x3y) * dx + -1(4xy3 + x4) * dy = 0 Reorder the terms: (2x3y + 5y4) * dx +…

Q: dy Write down a differential equation of the form dx 17 all other solutions diverge from y = as t →…

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Q: Does the following series converge or diverge? 4√√n Σ 3/2 10n +7n+7 n=1 O The series diverges. The…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 1. Find the Inverse Laplace Transforms of the following. 3) 3s³+3s s6 3

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Q: 16. Evaluate ft tan5 x sec¹ xdx.

A: We know that Sec²x = 1+ tan²x ∫ xn dx=( xn+1)/(n+1)

Q: 2. If ƒ (x) dx = = 4 and 3g(x) dx = −9, evaluate [*² [3ƒ(x) + g(x)] dx -2

A: Topic = Integration

Q: Evaluate the double integral: y SLAZ+1 y²/3 x + 1 (Hint: Change the order of integration to dy dr.)…

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Q: Differentiate the function. f(x) = x²(x + 8) f'(x) = x³ (x + 8) 3 X

A: In this question, we need to find the derivative of the given function.

Q: Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed…

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Q: Prove the following using the principle of mathematical induction. For n > 1, 1 1 1 1 = + + + 54 ( –…

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Q: Evaluate the following 3 3 x4 + 2x³ + 3 X² + x + 1 x4+x² 2

A: We have to evaluate the integral.

Q: 1. The simple interest charged on a 60-day loan of Php 8,400.00 is Php 119. Find the simple interest…

A: Use simple interest formula

Q: Find S dx √X²-2x+1

A: ∫1x2-2x+1dx=∫1x-1dx=lnx-1Add a constant to the solution=lnx-1+C

Q: The function f(x, y) = x² + y² √x² + y² +1-1' (a) {(x, y) = (0,0)} (b) {(x,y) = R²2} 2 if : (x, y) =…

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Q: 2. Find the total area under the curve f(x) = 2xe² from x = 0 and x = 5.

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Q: II. Find the inverse of each matrix. 5 -11 -9 1. -7 DO 8

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Q: estions 14 refers to data given below A certain radioactive material is known to decay at a rate 1…

A: Given problems:- A certain radioactive material is known to decay at a rate proportional to the…