1. Solve the following equations: c) (x² - 4xy – 2y²) dx + (y² + 4xy – 2x²) dy = 0 -

Q: (CLO-1) Find the values of a and b such that the following function if x 1. X-1 D=

A: Topic:- application of calculus

Q: The following Exercise asks you to find the area between two curves. To achieve this, we have the…

A: Solution is given below:

Q: Given R(t)=4 cos ti + (1+3cost)j +5sintk. Find T'(t).

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Q: What is the area of the region between X |y=x2–2x−3 and the x-axis from x=0 to x=4?

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Q: Consider the equations 2x - A) x² - 2x x³ +8 0 and B) = 0. x³ - 8 Which of the following statement…

A: We can find the answer in the following steps.

Q: - 1/2 Find the gradient of f(x,y,z) = (x² + y² + z²) 23 23 26 Vf|(- i+ - (-2,2,-1) 54 |j+ 54 27…

A: The function is f(x, y, z)=(x2+y2+z2-1/2+ln(xyz)  The point is (-2, 2, -1)

Q: Suppose that sin(θ)=4/6. What cos(θ)=______. (round to 3 decimal places)

A: sin(θ)=4/6

Q: 6 Consider the three by three system of linear equations 2x + Y + + 2y + 2z 5z 12. We will solve…

A:

Q: 2 3s +9 Option 3 23 -e³t e-3t Option 4 None of the choices Option 2 Option 1 2 -3t 3 3 N|W 2 co

A: As we know the inverse Laplace transform identity; L-11s-a=eat   Given: Fs=23s+9

Q: (-2, 39) -4 10 20 10 10 -20 89 -30 1 (14) (27) 23 Solve the following problems. A. Given the graph…

A: Given ,  Graph of function (4) We have to tell local minimum value

Q: Syy-mat sama dy ³

A: Follow the procedure given below.

Q: 3. Let R be the region below bounded by the parabola y = 4 – x² and the lines 3x - 2y + 3 = 0 and y…

A:

Q: The area between the curve y=x2, the y-axis and the lines y=0 and y=2 is rotated about the y-axis.…

A:

Q: For numbers 4-5, consider a plane bounded by the curve x = -y² + y +2 and the y-axis. The…

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Q: 2. 8 2 + (-1) 5+

A: Here we have ∑k=1∞2+(-1)k5k

Q: Solve the differential equation y"" + y = 3x² + sin x - 2 cos x

A:

Q: 2. Evaluate: S 0 trư √2 = x + x dx

A:

Q: Find the Laplace Transform of the following functions

A: Laplace Transform of function cos3t

Q: Find the value of the following implicit derivative tan y-sec x=5 find...y'

A: Given  tan y - sec x = 5 We have to find y'.

Q: Find the particular solution (D² + 4D + 4)y=0 when x = 0, y = 1 and y = -1 What is the particular…

A:

Q: If A = 3ai +4j-k and B=4i+j-3k, find the value of a if A normal to B.

A: Given A→=3ai^+4j^-k^  and B→=4i^+j^-3k^

Q: find area between line y=-2+x and y=x^(1/2) and x-axis 26/4 O 23/6 O 36/2 O

A: Here we have given equations of two lines as  : y=x and y=x-2.

Q: 9x3+3x²-12x Solve for the vertical asymptote/s of f(x) = 9x3+30x²+24x

A: To find vertical asymptote we will put the coefficient of y equal to zero.

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

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Q: Let f(x) = 5x² - 2²/2 + 8√√x-²3 (a) Find f'(x) (b) Find an equation for the tangent line to the…

A: As we know that; The equation of the tangent line is: y-y0=mx-x0 Where m is the slope of the tangent…

Q: SCcos2x + 2sin x)² dx

A:

Q: 5s + 4 83 2t5t³ Option 4 None of the Choices 2t + 5t³ Option 3 Option 1 5t + 2t³ 5t - 2t³ Option 2

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Q: 3 3. √√26.91

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Q: This question is designed to be answered without a calculator. If g(x) = si sint dt, then g'(x) = 0…

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Q: [CLO-3] The second derivative f"(x) of a function is given. Use this information to determine where…

A:

Q: In the following problem, begin by drawing a diagram that shows the relations among the variables.…

A: Use partial derivatives

Q: Find the gradient of f(x,y,z) = (x² + y² + z²) 23 26 Vf|(-2,2,-1) = i+ 23 54 |j+ 54 27 (Type…

A:

Q: 5. Solve the equation = 170. 6. Solve the following logarithmic equations. (a) log, (+5) = log, 3…

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Q: Q2/Find the value of the integral fx by using simpson method (n = 6)?

A: This is a problem related to integration using numerical method. Based on the general formula of…

Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x² + y² =25 and…

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Q: S52² +32° +22²-32 +2) dz

A: Solving the problem by finding the value of integration.

Q: Additional Activities (-2.39) a 4 88/88 20 10 10 -20 30 40 1 (2.7 Solve the following problems. A.…

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Q: 3s - 8 4s² + 25 3 8 25 -sin COS Option 1 None of the Choices 2 4 (sin t) - 25 (cost) Option 5 8 25 3…

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Q: Consider the following matrices: [2 3 id -1 27 - - A = B = 3 0 C = 1 0 b 4 1 Perform the following…

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Q: (CLO-3) Find the absolute maximum value of the function f(x)=x³-12x+3 on the closed interval [-4,3].

A:

Q: Find the average rate of change of the function over the given interval. f(t) = 13+ sint a. 0, 플] п…

A: As we know that; The average rate of change between the interval t1≤t≤t2 is given by: Average rate…

Q: {CLO-3} The function f(x)=2x4-4x² has a local maximum at x=-1; and a local minimum at x=0 has no…

A: Topic:- application of derivatives

Q: If given f(3) = -1 and f'(3)=5, the tangent line to the graph y = f(x) at x=3 is y = 5x +16. (a)…

A: This question is based on finding tangent equation at a point on function.

Q: calculator. Use this graph of function f. y at X = O conly. Od only. Oc and d only. O a, b, c, and…

A: Topic:- function

Q: Q1): Prove that: A square matrix B has inverse if and only if determinant of B is not equal zero.

A:

Q: 1 = and find x 1 Use linear approximation, i.e. the tangent line, to approximate as follows: Let…

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

Q: What are the rectangular coordinates of the point whose spherical coordinates are (1,,)? x = 0 y = z…

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Q: Find all the relative extreme values in the domain of y = tan(x)

A: Find all the relative extreme values in the domain of y = tan(x)

Q: We know that for some real number k, the function 3ekx is the solution of the second- order…

A: This question can be solved by substituting the value of y in the given differential equation.

Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² + 1 a. (4,1) b. (1,1)

A: To find the linearization Lx, y of the given function at each point.fx, y=x2+y2+1 a 4, 1b 1, 1