Find a gradient of the equation: F(x, y) = y + x³ – ay? + 3 %3D VF =?

Q: 11. If F(z) = | V1+4t² dt, find F'(x) sin z

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: Recall:  L=∫abr(θ)2+r'(θ)2dθ We have, r=7sinθ+2cosθ, a=0, b=π

Q: 135 5. y = x³, y = x + 6, and 2y + 2 = 0 (Answer: S. u.) 4

A: The region bounded by the curves y=x3, y=x+6 & 2y+2=0 is:

Q: Evaluate the following limits. If needed, enter oo for oo and -oo for 00. /3+5x2 (a) lim 3+11a V3 +…

A: LetL=limx→∞ 3+5x23+11xDivide x on N and DL=limx→∞ 3x2+53x+11L=limx→∞ 3x2+5limx→∞…

Q: dy - cosec'x. cos x (i) By differentiating 6 show that if y = cot x then sinx' dr (ii) Show that x…

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Q: 8. Find the dimensions of the largest-volume cylinder that can be inscribed in a sphere of radius 10…

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Q: dx x3 4. Зх2 + dy y+1 -8(у + 1) %3D 0

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Q: Find the following: (a) Sum of the first 21 terms of the sequence: 5,9, 13, 17,...

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

Q: answer does not exist, explain why. x - 1- V3x +1 a. lim- х — 5 1- x b. lim (x – 6)²

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Q: Q1\ Differentiate the following (choose two only) 1)z = sin (3x + 1) 2)f (x) = 3cot-12t 3)y = e 8*…

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Q: Q1\ Differentiate the following 1)2xsin-13x x+1 2)y = In Vx-2 1 3)y = sin-1 2x

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Q: Evaluate the following expressions. 12 6. a. Σk b. Σ ( 3k+ 2 ) d Σ (2+) с. k= 1 k = 1 n = 1 8 4 5m…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: Let y tan(3x + 6). Find the differential dy vwhen a 2 and da 0.4 Find the differential dy when z 2…

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Q: Show that the following functions satisfy Laplace's equation 0. dy? %3D (a) f(r, y) = r*y – xy³

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Q: Find the 11th term of the arithmetic sequence. $1264.02, $1946.38, $2628.74, ... a11 = $ (Type an…

A: This is a problem of arithmetic series. Please follow the procedure given below.

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

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Q: Q 25-The Laplace transform of function f(t) = e¯'sinh4t is a) 2/(s²+2s) b) 2/(s²+2s+15) Q?-The…

A: To Find : laplace transform of f(t)=e-tsinh(4t)

Q: Given the graph as below: ea Write the adiacency matriv for the granh (i)

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Q: 3. A curve has equation y = Find the x-coordinates of the stationary points of the curve in the tan…

A: To solve the following problem

Q: B2. dx Let g(?) = " 4t

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Q: (9) If f(x) = 2x +k and g(x) = (x – 5)/2, for what value of k is f(g(x)) = g(f(x))? %3D (A) 15 (B) 5…

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Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs x = y and x =…

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Q: 1. Determine the following using the graph of f provided below. If the value is infinite, specify o∞…

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Q: compete Mž uing Values ा. ड 2 12 64 X010.5 511o5

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Q: Please

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Q: Perform a first derivative test on the function f(x) = x/25 - x;(-5,5]. a. Locate the critical…

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Q: dy Plot the slope field for the differential equation dx = y?- - x and sketch the solution for the…

A: Solution is given below:

Q: 12. Solve the second-Order differential equation: -y = e* (use method of variation of parameters)

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Q: * This matrix is a 4 4 0 4 zero matrix O square matrix diagional matrix O unit matrix O

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Q: 2) Find the sum of the first 100 terms of the arithmetic sequence: 2, 4, 6, 8, 10, 12, ...

A: The arithmetic sequence: 2,4,6,8,10,12,.......

Q: Ballast Dropped from a Balloon A ballast is dropped from a stationary hot-air balloon that is…

A: Given query is to find the height of the blast after t time and the time when it will hit the…

Q: Evaluate f x3 using substitution (3–2x)5

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Q: Let V = R2. For (vị , v2), (W1, w2) E V and k ER define vector addition by: (vi, v2) O (W1, w2) :=…

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Q: 2) Find the absolute maximum and minimum values of f, if any, on the given interval, and state where…

A: We know that for absolute maxima and minimum value we do derivatives. We know that derivatives of…

Q: If the change of variables u = x -2 is used to evaluate the definite integral f(x) dx, what are the…

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Q: 1) Find the explicit formula of an arithmetic sequence with the given property. d = 12, and a6 = 68

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Q: Determine the resultant of the force system shown in Fig. 224 300 1 2 30 361 3.

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Q: Differentiate the following (choose two only )( 5 .. ) 1)2xsin-13x x+1 2)y = In Vx-2

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Q: 6) Let sin 0 - for n <0 < Find the exact value of: %3D 2. a) cos 0 b) tan 0

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Q: If y = a + b/x , then the linear form of the following equation is

A: We can solve this as follows:

Q: 72-1 b) En=1an for an 5. )** 00 %3D

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Q: For the given points A, B, and C find the area of the triangle with vertices A, B, and C. A(4,7,2),…

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Q: A roctangular tonk uith a cauaro boco and a volumo of 2.016 e3 dimoncions of tho tank that hac 1o…

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Q: Jacinta wants to use milk and orange juice to increase the amount of calcium and vitamin A in her…

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Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: Let's find.

Q: 3x - - 4y 2xy 96

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Q: 1 15. Find the first four terms of the Maclaurin polynomial for f (x) Express this series in sigma…

A: We have to find out series

Q: Consider the function: (x^2)/(x^2-4) 1. Find the domain of f. (Using interval notation) 2. Find…

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Q: Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid…

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