Use Lagrange multipliers to find the point on the plane x – 2y+ 3z = 6 that is closest to the point (0, 1,4), and enter it as a 3×1 matrix in Ans.

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A: Given query is to find the value of the integral.

Q: Example:- Find the general solution of 1) xdy – ydx = 0 2) xcosh(y)dy – sinh (y) dx = 0 3)2dx –…

A: We need to find general solutions.

Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use ∞ or…

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Q: f is just that e*-sin(x + y) + cos(x +y)] and = -e* sin(x + y) which if the ollowing is true Select…

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Q: In which limits below can we use L'Hospital's Rule? x – 2 lim 1→2 In(3 – æ) 1- et lim 2-0 sin(5x)…

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Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: State where the power series is centered. (-1)"(2n – 1) „n Σ * 2"n! n = 1

A: Solving

Q: 8. Find the limit: lim E1(1 130 noisieoq Isisinle bna baoes 1aq d00

A: The detailed solution is given below Thank you

Q: Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downwa O…

A: a.   Parabola opens downward   b. Coordinate of vertax. Is (-2,-3)

Q: e3t – 1 lim t0

A: Use l hospital rule for finding the limit.

Q: 8. Find y'ifys34-7x+2)+4%-2

A: Differentiation

Q: V3x - 2 lim tan- %3D x + V3

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Q: The average value of f f(x)dr if c =

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Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 6x, y = 0

A: Solution 1.  Given y=-x²+6x  And y=0 Now intersection point -x²+6x=0 X(6-x)=0 X=0 and x=6 Points…

Q: Showing all work, use the method of your choice to find the volume of the solid obtained by rotating…

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

A: solution:-limx→1sinx-1x3+4x-5 ,  it is  00   formusing  L'Hospital's…

Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: 7.372 The rate of change of the weight of a mouse, can be modeled by r(t) grams per week, where t t…

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Q: sec 1.)S Intanßtanß dß

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Q: Solve the following differential equations: d³y dy d?y 3- + 3 dx2 В. dx3 dxy=4e*

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Q: Find the direction angle of v for the following Vel v = - 6i- 3j What is the direction angle of v?

A: On solving this we will get

Q: lim sec x x-(-71/2)"

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Q: Find the roots Lzerel of eah tunction and State tHhe multipicty of any veputed root - 니 2x

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Q: (H.W) 1- Solve by choose M this time ( 2 x y² + 3 x² ) dx + ( 2 x² y + 4 y³ ) dy = 0 2- Find the…

A: If the differential equation Mdx +Ndy =0  is exact ∂M∂y=∂N∂x , then solution is                 ∫y…

Q: F(x) = e2x C = 0

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Q: A job applicant estimates that his chance of passing a qualifying examination is , and his chance of…

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Q: Given f(x, y) = 5z² + 42°y° – 2y“, find fr(x, y) = fy(z, y) = fer(1, y) = fry(x, y) = %3D

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Q: A ball is thrown into the air and its position is given by h(t) = - 4.3t2 + 41t + 15 where h is the…

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Q: system which is represented by the given equation below, is able to work effectively ven when the…

A: Given, f(x) = 7x ^ 3 - 0.31x ^ 2 + 8x - cos(x).

Q: 18. Sand is falling into a cylindrical tank at a rate of 15 cubic feet per minute. The radius of the…

A: Please follow the next step.

Q: Step 1 To find the definite Integral 9 dx by the limit definition, divide the Interval [2, 7] Into n…

A: For the asked steps we can solve as follows.

Q: 3. Find the binomial series for (1+x)3 4. Use the result in problem 3 to give a power series…

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Q: Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x² – 3x + 8…

A: Here We have to use the definition of the derivative.

Q: Find the standard form for the TANGENT PLANE to the surface: : = f (x,y) = x cos (xy) at the point…

A: The given function is  z = f(x,y) =x cos(xy)

Q: The Mean Value Theorem states: For any function, f, differentiable on (a, b) and continuous on [a,…

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Q: Step Solve for c. Use inverse trigonometric functions to find the value of c guaranteed by the Mean…

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Q: Find the length of the curve. 8) The spiral = e20, 0 s 0 s Ti r

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Q: sin ® 3y cos3ydy cos 3y dy

A: We have to find out the integral

Q: Find the derivative of: 3 sin (– 3x). Hint: sin (x) = [sin(x)]"...so use the chain rule (twice!).

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Q: Find the differential dy and evaluate dy for the given values of x and d.x y = Vx2 + 24, x = 1, dx =…

A: First differentiate with respect to x then find value at x=1 and dx=-0.1

Q: y 4 (2, 4) y = 2x y = x2 2 Using a vertical element of area, the area of the shaded region is given…

A: Solve the following

Q: Problem 7. Solve the equation logx+log(x+1) = log12 and leave your answer in exact value

A: Solve for the value of X

Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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Q: Use series to evaluate the limit. 4 3 sin(2x) – 2x + lim 4/3

A: Given problem:-

Q: Step 3 Apply the Fundamental Theorem of Calculus, which states that f(x) dx = F(b) - Fa). Use this…

A: We can complete step 4 by the cross multiplication method.

Q: Step 2 Fx) dx = 1 To evaluate f(x) dx, substitute f(x) c In = - Therefore, f(x) dx =

A: We have to evaluate given integral

Q: Find the length of segment AB. Round your answer to the nearest tenth. A 51° 26° 20 mi B 15 mi 16 mi…

A: ANSWER: 16 mi SEE ATTACHMENTS

Q: d) Use the right endpoint rule to approximate the area under the curve of f(x) = 4- x2 on [1,2]…

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 00 1 3n3 n…

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Q: 6. The rate of growth of a particular population is given by dp 50t? - 100t3/2, where P is the…

A: Given problem:- The rate of growth of a particular population is given by (dp)/(dt) = 50t2 - 100t3/2…