3. f(x, y) = (3x - 5y)2 + e4x In(4y – 9) + %3D 135 x4

Q: Consider the following. f(3) = 9, f(-1) = -11 (a) Write the linear function f such that it has the i...

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Q: Let f(x, y) = xr sin(xy). Find (a) xy cos(xy) (b) y cos(xy) (c) x² cos(xy) (d) -x sin(xy) (e) Some o...

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Q: Assessment 1. Directions: Find the limit of the following. 8x+1 5. lim X-1 x+3

A: We know by definition of limit for a function f(x) , limx→af(x)=f(a) , provided f(a) exists.

Q: 4x -3 ifxs3 a. Graph f(x)= ifx> 3 b. Find f(1) and f(4) c. State the domain of the function a. Choos...

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Q: Find the minimum and maximum values of the function f(x, Y, z) = 3x + 2y + 4z subject to the constra...

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Q: r.(t) = (0.5, 14.5, 0.5) + t (1,3, 3) r_(t) = (-6, 11, –1) +t (-2, 2,3) %3D Find the point of inters...

A: Given problem:-

Q: 2 = In (e*x³) 12.

A: As per our guideline we can answer only 1 question so kindly repost the remaining questions specifyi...

Q: Determine whether the two given vectors are orthogonal, parallel, or neither. u = (4, 5,-2), v = (3,...

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Q: 3 Evaluate y cos (z') dx dy dz

A: Explanation of the answer is as follows

Q: 1 dy : ? If Y = x² then da 222 2x

A: Since the student has posted multiple questions and does not mention any specific question, so we ar...

Q: Directions: Evaluate the following limits. 3. lim ) 4. lim ) x-1 x2 X+4

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Q: Find the arc length of the parametric curve. x = cos' t, y = sin° t, z = 2; 0 < t < T/2

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Q: sin x 5. Use series to evaluate dx .

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Q: Use algebraic and/or graphical methods to solve the inequality. 10x° -x* <0 Select the correct choic...

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Q: Give two other polar coordinate representations of the point, one with r 0. (r, 0) = ( 3, – 2.14 X ...

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Q: Use the Geometric Series Test to show that 0.3+0.03+0.003+…… converges.

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Q: Determine whether the variation model represented by the ordered pairs (x, y) is of the form y = kx ...

A: here it is the y = k/x form and  now k = y*x put the value  k = 4*1 =4 k = 8*1/2 =4 k 12*1/3 =4 so f...

Q: 2. Determine the derivative of f(x) = sin-'(2x)

A: Topic = Derivative

Q: Determine whether the integral is convergent or divergent. 7z2 In(z) dz convergent O divergent If it...

A: To determine: Whether the integral is convergent or not. Given information: The integral is ∫027z2ln...

Q: cot (5 + 7y) dy 2, 3.

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Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 6  where the tangent line is horizontal.

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Q: 3 5 k3 5 d. k 225 k=1 k=1 EG+ 2n) е. k=1

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Q: Calculate the derivative using implicit differentiation: dw x'w + wt + wz² + 4yz = C dz ||

A: Given problem:-

Q: 8) Find the critical points then sketch the graph of the function below. Provide the first derivativ...

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Q: 1. Determine whether the following series conv. or div. (n+4)! a. Ln=1 4! n! 4n 1 1 b. En=1 4n 2" co...

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

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Q: Find the area of the triangle with vertices P(1,2, –2), Q(0,0,0) and R(2,3, 1). NOTE: Enter the exac...

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Q: 6 f(16) = 63. X, f'(x) =

A: answer of given question is in step 2

Q: Use the fact that the volume of a tetrahedron with adjacent edges giv by the vectors u, v and w is 1...

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Q: Evaluate lim x? (e - 1) using series . X00

A: We know that ex = 1 + x + x22! + x33! + ⋯

Q: 00 (-3)* Consider the series > ak= k5 k=1 k=1 a) What is ak+1? ak-1 = ak+1? b) What is ak ak-1/a = a...

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Q: 4. Find Maclaurin series for f(x) = xex . %3D

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Q: y" – 2y' + y = -3 – x + x², y(0) = –2, y'(0) = 1. %3D %3D

A: Given: y''-2y'+y=-3-x+x2 ; y0=-2, y'0=1 So, We can also write as; D2-2D+1y=-3-x+x2   The auxiliary e...

Q: Use the fact that the volume of a tetrahedron with adjacent edges giver by the vectors u, v and w is...

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Q: 4 – dt 2 cos 4t 1.

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Q: Find the slope of the tangent line to the circle 4x² + 9y² = 36 at the point (0,2).

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Q: x = r° +1, y=r -t a) Find dy/dx

A: To find the derivative of given parametric function.

Q: 2–3 Find |u X v and determine whether u X v is directed into the page or out of the page. 2. |v|= 5 ...

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

Q: Consider the following. 1 = (3, 7), v = (4, 6) (a) Find the projection of u onto v. 27 13 (b) Find t...

A: Given vector,u=3i+7jv=4i+6jVector projrction of u on v=u.vv2v=(3i+7j)(4i+6j)42+62(4i+6j)=12+4216+36(...

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does...

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Q: Find the derivative of the following including trigonometric identitier functions. Show complete sol...

A: h = sin-x here we apply chain rule dh/dx = (1/2sin-x)*(1/1-x2) dh/dx = 1/2sin-x*1-x2   y = k2sin-(x/...

Q: Find the characteristic equation and fundamental solution set to the di fferentinl equation 4 +4

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Q: J E1 = (J – 2) i = 3

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

Q: Differentiate y = sin (x-y)

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Q: In a local art museum, a moving spotlight projects geometric figures on the wall in front of it. The...

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Q: The widths (in meters) of a kidney-shaped swimming pool were measured at 4-meter intervals as indica...

A: We have to calculate area using Mid point Rule.

Q: 2. Find the interval of convergence of En=1 n(n+1)

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Q: Determine whether the two given vectors are orthogonal, parallel, or neither. u = (9,3), v = = (-2, ...

A: We can check whether the two vectors are parallel, orthogonal or neither by definition as below.

Q: rectangular box without cover has a volume of 12 m?. The width of the base is half Hhe length. Mater...

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Q: dy 21 z'e ", by using Variable Separable de PROBLEM [ B6 (b) ]: Solve the first order differential e...

A: Given the first order differential equation is dydx = 21x2e-y