Find an equation of the tangent plane to the surface 3x? + 2xy – 4z2 + 2x – 3y = 0 at the point P(0, –12, 3) -

Q: I +1 5. h(a) at x = 1 x2 – 1 -

A: Factorize the denominator.

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x– y + z =…

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A: Topic = Circle

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A: The objective of the question is evaluate the vector.

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Q: 3. -2 -5 Find the va lue of Hif Xi+xdx 3.

A: 3-2-518H-134=∫03x1+x2dxPut 1+x2=yas x →0 ,y→1as x →3 ,y→2differentiate on both…

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A:

Q: 5. Given the function as f(x,y)=\x² +y² then find the a) Rate of change of f at point P(1, ) in the…

A: This is a problem related to derivative of the function. Based on the general formula we will solve…

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A:

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A: To find gradient of the function at the given point.

Q: Convert to an equation in rectangular coordinates. r = 4 csc (0) – sec (0) (Express numbers in exact…

A:

Q: Find the directional derivative of the function at P in the direction of v. h(x, у, 2) %3D хуz, P(4,…

A:

Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 22 — 0. - NOTE:…

A: Find the distance between the parallel planes.

Q: Use Lagrange multipliers to find the indicated extrema of f subject to two constraints, assuming…

A: Given :Max f(x, y, z) = xyzConstraints :  x + y + z=24, x-y+z=8To find : x, y and z are…

Q: For each of the following functions, determine whether the function is: • Injective (one-to-one). •…

A: We have to check whether the function is Injective, Surjective or Bijective.

Q: sin4x S V cos4x + 1 dx

A:

Q: Find and classify the critical points of the function f(x, y) = x² + 2xy+ 3y + 2x +y . %3D O (-2,1)…

A:

Q: Cosx sinx 1+sinx

A: The given integration is ∫cosx sin2x1+sinx dx We solve the integral by proper substitution. Let,…

Q: For the following data set, find the regression line without using a calculator. x 1 2 3 4 y 26 8 9…

A:

Q: Find the cofactor of the element a13- -2 -1 0 5 4 2 3 5 O A. 3 О В. 19 ОС. -3 O D. 14 3.

A: Given a square matrix, the cofactor of aij is denoted by Aij=(−1) ^(i+j)M where Mij s the minor of…

Q: 2. f(x) = x² - 5x + 6 A. x = 1 B. x = -3

A: This is a problem related to limit and continuity parts of the calculus. Based on the general…

Q: Given: f(x) = with f'(x) = r(x+8)(x – 2) and f"(x) = 8(7x – 4) %3D (r+2)² ' (r+ 2)³ (r+ 2)ª (a) Find…

A: Note: Since, the student has mentioned to solve only part (a), so we are going to solve only part…

Q: Find an equation of the plane that passes through the points (3, 3, 5), 2, 2, —1), аnd ( —5, 3, 4).…

A:

Q: In 2000 the population of the United States was 280 million and the number of vehicles was 200…

A:

Q: Given y = Vx – 2/x – 2; Find y'. O (E) None of the choices Vz-2-1 y = 2/(z-2)(x–2/z-2) VI-2–1 2(x-2)…

A: Given: y=x-2x-2   We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x

Q: > (-1)" x3n+2 find the exact value of 5-1)"(3n + 2) By differentiating the power series 8n n=0 n=0

A:

Q: Consider e" S- for all a E R. a. Determine the power series representation of f(x) = xe-5x² for all…

A: We have given the power series of ex  ex=∑n=0∞xnn!  for all x∈ℝ

Q: Use Lagrange multipliers to find the maximum and minimum values of subject to the given constraint.…

A:

Q: Find the directional derivative of f at the point P in the direction of a. i-j f (x, y) = 2x3 – 6y³;…

A:

Q: 4 3 1 10 15 20 25 30 35 time (sec) feet velocity (ft/sec)

A: At t=0, velocity is 1 ft/sec. At t=25, velocity is 3 ft/sec. Required distance =Final velocity -…

Q: (3y²+ 2x³)dy + 2xydx=0

A: As we know that; The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. The solution…

Q: x2 – 1 6. g(x) = Vr – 3 at r = 4 - %3D

A:

Q: Convert xy = 7 to an equation in polar coordinates in terms of r and 0. %3D (Express numbers in…

A: Given query is to find the the polar form.

Q: 3. -1 1 2 3 4 5 6 7 +1

A: To approximate the area under the curve graphed below from x=2 to x=5 using a Left Endpoint…

Q: 20x at P(4,0) in the x + y Find the directional derivative of f(x,y) direction of Q(2, –1). NOTE:…

A: The expression for the directional derivative of the function f in the direction of u is:…

Q: 4. x - 3

A:

Q: Given: h (t) = Find h'(t). t² +2 O (E) None of the choices -8t3 O h (t) (1²+2)* O h (t) = 8t° (1+t*)…

A: Use quotient rule for differentiating h(t)

Q: Integrate x sqrt of (x+4) dx using algebraic substitution

A:

Q: Barbara boards a Ferris wheel with a 50-foot radius. The center of the Ferris wheel is 60 feet above…

A: Given information:…

Q: Determine if the following statements are true or false. (a) A square matrix has an inverse if the…

A: Here,   We have given some statements about matrix now we have to determine whether they are true or…

Q: 8. f(x) = (6x² + 7x)* 9. f(t) = (4t² + 3t + 2)-2 10. f(x) = (5x* – 7x)2/3

A:

Q: Problem 2. Which gives the inverse transforms of the given s-domain function? s2-s3+3/s3(s+5)(s-2)

A:

Q: Match the graph of f, below, with that of its derivative. -2 -1 1 2 3 4 1- -2 4 6 -4+ -3- -6+

A: This question is related to Functions and its derivative, we will solve it using given information.…

Q: Find an equation of the curve in the xy-plane that passes through the point (2, 3) and has, at every…

A: integration

Q: Compute the partial derivatives shown for the given function. 5 ху f(x, y) = + ; find fy, fy, and…

A:

Q: B. Determine the slope of the tangent line at a given value of x. 6. f(x) = x 7. f(x) = -4x3 – 2. 8.…

A:

Q: Given the function f(x) = () a) Find a power series representation for f(z). п(п + 1) (n + 2):…

A: Let's find.

Q: -4 X+

A:

Q: 2. a) Find lim g(x), lim g(x) and lim g(x) x→1- x→1+ x→1 b) Find f(1). c) Is g continuous at x = 1?…

A: Follow the procedure given below.