Use continuity to evaluate the limit. 16 + Vx lim 16 + x

Q: Let f (x, y, z) = xyz. Determine the value of fryy + fyay – 2 fyyr Simplify your answers.

A: We have to find the value.

Q: Current Attempt in Progress Use Green's Theorem to evaluate the integral. Assume that the curve Cis…

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Q: 1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

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Q: EXAMPLE 6 Evaluate the following integral. tan (r) dr SOLUTION First we write tangent in terms of…

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Q: The depth of the water in a cylindrical tank 4 m in diameter is increasing at the rate of 0.7 m /…

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Q: Question 6 Determine the derivative, y': y = log, (In a?) %3D Oy = z In 5 In a Oy = = z In 5 In z Oy…

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Q: 2. Given the DE as (x² + y² – 3)dx – 2xydy = 0 a) Prove if the given DE is exact or non-exact b)…

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Q: 4. By implicit differentiation , find the 1st derivative of x3 + y3 + 6xy = 0

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Q: 1 Find the area onclosed by the Curve r=4-3 sin 0.

A: Area

Q: 11 ti + dt

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Q: Evaluate the line integral - -ydx + xdy along the curve C : y? = 3x from (3, 3) to (0,0). NOTE:…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 5…

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Q: y= In e+1

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Q: (ye» dy Ans. (3e* +1) 4 11. 0

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Q: Question 10 sinh a For y= V find y' at x = In2 e* Oy = 0 Oy = 12 Oy = 2/6 Oy =

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x + 3 lim x--3 x + 27

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Q: When the eigenvalues of a b A = 0 d are 2, = 0 and 2, = 2, what are the possible values of a and d?…

A: When the eigen values of A=ab0dare λ1=0, and λ2=2, then to determine the possible values of a and d.…

Q: Use power series operations to find the Taylor series at x= 0 for the following function. 17x e* The…

A: we want to find taylor series of the function 17 x ex  about  x=0

Q: 5. [sin-' x dx Ans. x sin'x - V1-x² +

A: We will use integral by parts to evaluate integration of arc sinx

Q: Find the indefinite integral. (Use C for the constant of integration.) 5 tan(7x) sec2(7x) dx

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Q: In 1 decimal place Find the Surface Area generated by rotating the first quadrant portion of the…

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Q: 5. By Chain Rule , evaluate a. y' for y = u? + 4u and u = 4x3

A: This question is related to Differentiation, We will solve it using given information.

Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: Find the value of dy/dx at (1,0) of 2re" – In() = 4y² + 2a sin

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Q: Find the root of x4-x-10 = 0 approximately upto 5 iterations using Bisection Method. Let a = 1.5 and…

A: The root of x4-x-10=0 between a=1.5 and b=2

Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

A: Given problem:- Find the conservative vector field for the potential function by finding its…

Q: 0.4x Find the area between the curves y = e and y 1.9x + 1 from x = 0 to x = 3. Area =

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Q: Find div F and curl F if F(x, y, z) = 13y'z4i – 16x4z10j – 3xy'k. - - div F= curl F=

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Q: Question 2 Find the inverse Laplace transform of H(s) - (;+)-

A: H(s)=1s2-e-s1s2+2s+e-4s4s3+1s L-1{H(s)}=L-11s2-e-s1s2+2s+e-4s4s3+1s…

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

A: Given that,       r1(t)=9t i+4t2j+5t3k,   r2(t)=t4k

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: S*r(sin³x cos x + sin x cos x) dx -- 4 Ja sin 50 de

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Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it converges…

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Q: Find both first partial derivatives. z = Gy?V az az ay

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Q: 2. (Section 9.2) A refinery produces both gasoline and fuel oil, and sells the gasoline for $4.00…

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Q: 7. [x' In? x dx (9 In' x- 6 In x + 2) +C Ans. 27

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Q: Find dy/dx. x = Vt y = 9-t dy dx

A: Here, x=t3y=9-t

Q: Find curl (4z i+ 5x j+ 9y k). curl (4z i + 5x j + 9y k) = ( Di + ( j + ( i i )k

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Q: Question 3 dy Given the following function, determine do sec 0 You may use Insert -> Equation to…

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Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). ||r(t)|* 13 r(t) = t’i + t°j K(t) =

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Q: dx x² + 4

A: A detailed solution is given below.

Q: Find div F and curl F if F(x,y, z) = x°i – 11j + yzk. - div F= curl F=

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Q: 1 Which of the following is an antiderivative of the function f(r) = %3D 5+ x2 (a) 2x In(5+2?) 1 (b)…

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Q: dy Solve the separable differential equation dt t t?y + y Use the following initial condition: y(0)…

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Q: Graph in radians please

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Q: A function is defined as f(x) = x3 - x - 11 = 0. Between the interval [2,3] find the root of the…

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Q: 1. (Section 8.1) In surveying, it is often necessary to determine the height of an inaccessible…

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Q: Complete the table. (Use C for the constant of integration.) Original Integral Rewrite Integrate…

A: We can evaluate the given integral by using the following formula.

Q: , Evaluate by interpreting it in terms of areas. *P (2* – I^ + *),J

A: We have to evaluate integral by interpreting in terms of area

Q: Evaluate the following indefinite integral: x dx 1.) S- Vx4 - 1

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