xy³ Q3: Let f(x,y)=2x²+y² 1 (x, y) = (0,0) Is f continuous at (0,0) ? Is f continuous at every point ?

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

A:

Q: Evaluate the following * 5 Sa 4x - 1 In(4x - 1) 4 O II -dx + C 5ln(4x - 1) 4 + C 5ln(4x − 1) + C 4…

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Q: 1. Find the Inverse Laplace Transforms of the following. 4 1) -1 S-3

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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: Evaluate: 3₂₁ [2³(x + y)³] dz dy dx

A: Given: I=∫-23∫-12∫01z3x+y3dzdydx   As we know the Power Rule: ∫ax+bndx=ax+bn+1an+1+C, where a &…

Q: f(x, y) = x² - y² + 10x +12y - 64 −x² −

A: To determine the extrema if any for the given function.fx, y=-x2-y2+10x+12y-64

Q: t = b? Choose 1 answer: b Ⓒ / ° v A a © B Ⓒ a b cb a a b e20t+t6 dt e10t+t³ dt 10e10t+ 3t² dt…

A: Topic = Integration

Q: Use the table of integrals to evaluate the integral. 2 5x³√4x² - x4 dx

A:

Q: Let F(x,y)=ln(x² + y2), then answer the following (1) Find the function's domain (2) Find the…

A:

Q: hi what is the simplified final answer of this?

A: Given problem:-

Q: (x² - y²)²] 1²₁ 1² du du dt x+y Evaluate: ₁ S

A: Given ∫-13∫02x2-y22x+ydudt Since x2-y22x+y is constant with respective u and t, we take constant out…

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A:

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 =…

A:

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: (a) lim x→0+ (sina) 1 (b)…

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Q: Evaluate: 3₂(4x²y - z³) dz dy dx

A: On solving this we will get

Q: Evaluate: ƒ³₁ ƒ²₁ √√²[z³(x + y)³] dz dy dx

A:

Q: Determine y = Yc+yp using Non-homogenous equations: Method of Undetermined Coefficients Given: y" +…

A:

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

A: To find the volume of the solid that results when the shaded region is revolved about the indicated…

Q: -2 Evaluate: ²₁5²[(x²-²²] | du dt x+y

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Q: 2 убличк In'/xl alx

A:

Q: Given a second order differential equation dx 2x = e³t dt where t = 0, x = -5. Using Laplace…

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Q: Evaluate the following * [x√x² - 7dx

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Q: 3. The definition of Antiderivative states that A. A function (x) is called an antiderivative of the…

A: 3. The antiderivative of a function f(x) is a function whose derivative is equal to f(x).

Q: 5. Determine the roots of y"" - 3y" - y' + 3y = 0 a. 1, 1, 3 b. 1-1, -3 c. 1, 1, -3 d. 1,-1, 3

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Q: 5. Find and classify (local max., min. or saddle point) all critical points for f(x,y) = x³ − y² +…

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Q: Function h is graphed. ← -4 -3 -2 -1 Find ["h(2) dz. [²h(z) dz = [ Y 4 3- 2+ 1 -1 -2- -3- -4 h 1 2 3…

A: The given graph is:

Q: Q9. If W = f(u)=u³ +sin ¹u+lnu, and u= ax +by, where a, and b are constants, show that aw Əw b oy Əx

A:

Q: • show that (x, y, z) = PDE : 2²4 ахг 824 дуг + 2 x² + y² + z² = 0 8²4 dz² satisfies the

A: This question can be solved using the concept of partial differentiation.

Q: 2. Solve each of the following integrals using integration by part: a) √3x² In 2x dx b) 5x sin 3x dx

A: Integration is evaluated.

Q: Evaluate the integral by making the given substitution. (Remember to use absolute values where…

A:

Q: Q3 A) Write the first five terms of the following: - 2. {1- (-1)") (3n+2 B) Determine which of the…

A: "since you have asked multiple question,we will solve first question for you.If you want any…

Q: For each of the following ,find fx fy fxx fy fyx and fxy f(x, y) = x cos+ ye*. 2.f(x,y) = y²x¹e². 3.…

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Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: Differentiate the function. g'(x) = g(x) = 2x² - 8x + 13 gx 8 2 X Read It Need Help? Master It

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Q: (3) If R is an integral domain has non zero characteristic, then Char(R)=..... (i) 5 (ii) 4 (iii)9

A: Option (i)

Q: Question 3 Determine L-1 ¹ s²+3s-7 (S-1) (s²+2).

A:

Q: Given a second order differential equation dx 3t 2x = e³t dt where t = 0, x = -5. Using Laplace…

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Q: Evaluate the following * S sin(4x) dx O cos(4x)/4+C -4cos(4x) + C O-cos(4x)/4 + C O-4cos(4x) + C

A: We can find the answer as below.

Q: 3. Find the volume of the solid formed by revolving the region formed by the curve y = secx about…

A: Explanation of the answer is as follows

Q: Determine the values of r for which the differential equation y" - 4y = 0 has solutions of the form…

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Q: Evaluate the integral. ƒ ƒ6(x³ - y³)²dA = □ (Type an exact answer.) R

A: ∫-11∫016x3-y32dA

Q: Find the area of the region bounded by the curves y= (x+8)2 y = 4 and the x-axis using vertical…

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Q: What if you could predict one what your monthly income (USD) would be after graduation from the…

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Q: 1. Find the Inverse Laplace Transforms of the following. 4) 48-60√s s4

A: A detailed solution is given below.

Q: 62. y" +9y=e* cosx

A:

Q: Find the area of the region bounded by 2x and the y-axis using the horizontal strip. 3 y² +1

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Q: Evaluate: du [(x²-y²)²1 ³₁ 1² du dt x+y

A: Given , ∫-13∫02x2-y22x+ydudt

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

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Q: dy Solve the differential equation. X dx = y + x³ + 3x² -2 x

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Q: A- Answer the following L-1 3s-1 s²+2s+5

A: