2. Show that the function g defined by VVT y² + √² 2, is not continuous at (0,0). (z,y) = (0,0) (x,y) / (0,0)

Q: find the derivatives: 1. y= (tan x)/ (1 + tan x)

A: Solution: 1. y= (tan x)/ (1 + tan x) y'=ddxtan x1+tan x

Q: Solve the system of differential equations. = - X1 6x1 + 2x2 X2' - 2x1 - 10x2 2, x₂(0) - 22 = x1 (0)…

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Q: Solve the system of differential equations. X1' = 3x₁1 - 1x2 X2': = 1x₁ + 5x2 - 11, x₂(0) = 7 x₁ (0)…

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Q: Find the critical points and sketch the graph

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Q: 21 21 The two-dimensional Laplace equation = 0 describes the potentials and steady-state temperature…

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Q: Sketch the vector field F(x, y) = i + 3j and calculate the line integral of F along the line segment…

A: We have to sketch the vector field.

Q: x² dx -1 (2x²+2x+1)² sº₁

A: We have to evaluate the integral. ∫dxa2+x2=1atan-1(xa)+c

Q: -lving ³4xdx gives 4x b. 4x² c. 2x 1²³ C. 31 d. 2x² 1³

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx,…

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Q: Use the geometric series f(x) = convergence of the new series. f(x) 8 1-x 1 Σx, for x<1, to find the…

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Q: Solve the boundary value problem y" + 4y' + 13y = 0 y(0) = 0 y'(pi/2) = 0

A: To solve the given differential equation

Q: A lamina occupies the part of the rectangle 0 ≤ x ≤ 1,0 ≤ y ≤7 and the density at each point is…

A:

Q: An electric elevator with a motor at the top has a multistrand cable weighing 7 lb/ft. When the car…

A:

Q: 1. Find the third-degree polynomial P such that two of the zeros are 4 and 1 + i and such that P (2)…

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Q: Given cost and price (demand) functions C(q) = 150q+46,400 and p(q) = -2.4q+880, if the company sets…

A: Given that cost and price (demand) function C(q)=150q+46,400 and p(q)=-2.4q+880.Also, if the company…

Q: 3t4 - 6t+ 3et Let f(t) = Then f'(t) =

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Q: Find the derivative of cos-¹(sin x)

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Q: 1. Find the area bounded by: x=y² and y=-x²

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Q: 0 7 m We model pumping from spherical containers the way we do from other containers, with the axis…

A: To find the work done.

Q: open rectangular box with square base is to be made from 48 ft2 of material.  What dimensions will…

A:

Q: If the sides of an equilateral triangle are increasing at a rate of 6 m/min. How fast is the area of…

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Q: The time required for an elevator to lift a weight varies directly with the weight and the distance…

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Q: Determine el valor de a € tal que: 80 ex e2x + 1 58⁰ a -dx = R+

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Q: Evaluate the integral. 34 1 8- dx

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Q: 7) Find the absolute maximum and absolute minimum values of f(x, y) = 4x+6y - x² - y² on the set of…

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Q: Find the relative extrema, determine if it is relative minima/maxima, and sketch the graph. 6. f(x)…

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Q: S dx x² √√x²-1²

A: Follow the procedure given below.

Q: Find the derivative. f(x) = eº · 3x f’(x) =

A: topic- derivative of a function

Q: 2) For f(x, y, z) = xe²yz. (a) Find the gradient of f.

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Q: Sx". .n-1 +n[x²= x" sin x dx = -x cos x + n cos x dx

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Q: A product is introduced to the market. The weekly profit (in dollars) of that product decays…

A: First we rewrite the profit function in terms of t.Then differentiate p(t) with respect to t.

Q: Use the method of disks/rings to determine the volume of the solid obtained by rotating the region…

A: Given that the region is bounded by y=2x2 and y=x3 about the x-axis.

Q: Evaluate the definite integral. (7x² - 6x +9) dx 0

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Q: The entire graph of the function g is shown in the figure below. Write the domain and range of g as…

A: Find the domain and range

Q: TC √³x² x² sin3x dx

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Q: 10 = (+5x)dx 45x+9 -1 7/4 52 (+9) + 48 (x+g)' f(x+9) + 2

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Q: 1. f(t) = (t5+t) (t³ - 4t+1) 2. g(x) = (+1)(3x - 1) 3. h(x)=¹

A: Topic:- function

Q: For each graph, choose the function that best describes it. (a) (b) (Choose one) (Choose one) (C)…

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Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: Ths question can be solved using the formulas of Laplace transform.

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = In (√9-x²) dy =

A: Solution: y=ln9-x2 Differentiate both sides

Q: 4 -3 -2 -1 5 4+ 3 2 1 -1- ea -3- 4+ -5- 3 4 domain range = =

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Q: Given : f(x) = 10 -x 9(x) = x² - 4x-2 Find and simplify (fºg)

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Q: = A region bounded by f(x) X- 1/₁, y = 0, y = 2, and x = 0 is shown below. Find the volume of the…

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Q: Setan2 sec² 2xdx Select one: O a. 0.4325 O b. 0.0287 O c. 0.6543 d. 0.0177

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Q: Complete each of the following. a. Graph each function by making a table of values. b. Determine the…

A: We have to graph the following function.

Q: Find the point of the porabola y=x²-4x+3 where the tangent is parallel to the line 3x+y=2. Determine…

A: topic- equation of tangent line parallel to given line

Q: A. Evaluate the follow 1. S dy 3+√y+3

A: