dx ylnx dy || y + 1 X 2

Q: y=x² - 4x and y=-x²+2x.

A:

Q: Identify

A: Please refer to the image below

Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

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…

A:

Q: 3) Evaluate for ln(x + 1)dr

A:

Q: S 10dz 4z³-4z² + 5z

A:

Q: Determine the intervals on which the function is concave up or down and find the value at which the…

A: To determine the intervals on which the function is concave up or down and to find the value at…

Q: 5. √√64 .05

A:

Q: Show that the particular solution of the differential equation d²y dx² -6y-12(x+ e*) +5% dx 5 is…

A:

Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

Q: cos³ t

A:

Q: 4. A rock thrown into a still pond and causes a circular ripple. If the radius of the ripple is…

A: Follow the procedure given below.

Q: -4 -3 -2 -1 wo 4 -1 -2 -3 -4 -5 1 2 3 4 5

A: Slope is given.

Q: Use symbolic notation and fractions where needed.) a= b = C = d =

A: Topic:- calculus

Q: [9] Q4)(a) Find the maximum eigen value for the system 4 = x (0)=(0.02991) with initial vector

A: Follow the procedure given below.

Q: 8. Evaluate 2 (9x² - 10x + 6)dx

A:

Q: A. Find the general equation of the conic with the given properties. 51 1. A parabola with directrix…

A: Note: There are multiple questions. No specific question has been asked.So, We will solve the first…

Q: 2/ Find the equation of the tangent line at (0,0) to fex) = xex хе 2 -X

A: Given f(x)=xe-x2y=xe-x2Differentiate…

Q: 7) Find the critical point (s) of f(x, y) = 2x³ + 3y² - 9x² - 30y + 12x-3. Then use the second…

A: solution is given below...

Q: 1. The diagram shows a regular hexagon. Write a single vector that is equivalent to each vector…

A: Triangle law

Q: Solve the differential equation y""+y" = 3x² + sin x - 2 cos x What is the particular solution?

A: We have to find the particular solution.

Q: 1–2 = For each of the following functions given by power series, find f'(x) and f f(x) dx. Do not…

A:

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

A:

Q: [4pts] Consider a point in Cartesian coordinates given by (3√/3, -3, -8). a.) Find a corresponding…

A:

Q: -5e-cos2t O Option 4 5e-t sin 2t O Option 2 5e¹ cos2t O Option 3 5e sin 2t O Option 1

A: Topic:- application of derivatives and integration

Q: у4 61 -6 -5 -4 -3 -2 -1 $59 5 4- 31 2- -1- 0 F11 -2- M 23 -3- -4-1 -5- 56 -6- 1 2 3 4 5 6 m= Final…

A:

Q: Assume that the given figure is the graph of f'. y in

A: Local Maximum:It is a point within an interval at which function has maximum Value. Local Minimum:It…

Q: Consider the matrices shown below: A Find the value of K such that det (BT) 64 - 1 с 3K and AT is…

A:

Q: Differentiate the following function. f(x) = (x+2) e-6x +1 f'(x) = (Type your answer in factored…

A:

Q: Which of the following equations does not represent an ellipse? * x² + 2y² - 16 = 0 Option 1 x² +…

A: topic - equation of ellipse

Q: For the F(x) function shown in the figure, find P(0≤x≤0.5) F(x) 1 1 2 1 2 1 X

A:

Q: 3. The function f(x) = 5 is continuous at all points of its domain? x²-16 A. True C. Maybe B. False…

A: We know that The domain of a function is the set of input or argument values for which the function…

Q: gh (2,-5), parallel to y= 2x+4

A:

Q: 2. Evaluate: S 0 trư √2 = x + x dx

A:

Q: The equation of the tangent line to the graph of f(x)=ln|x at x = -2 is v=²(x+2)+n2 (a) TRUE (b)…

A:

Q: 4 None of the Choices f(t) 1 (e²+ e ²¹)-(e₁-e²₁) Option 3

A:

Q: zl 5. Trigonometric form of the quotient of = 6cis (2); z2 = 2cis () is:

A:

Q: The area between the curve y = 1/x, the y-axis and the lines y=1 and y=2 is rotated about the…

A:

Q: 15-18. Find the extrema of f(x) = 3x - 4x³ on the interval [0, 2].

A:

Q: 2. √√√x + y + xy = 21

A:

Q: Finding the rate of change of the function defined by y = x³ and evaluating it at x=9 units yields…

A: topic - rate of change of function

Q: Find 2 dr if y=1-t² and x= 4+² dx

A: 1.       dy/dt = d/dt [ 1- t²]   = -2t        2.      dx/dt  = d/dt [ 4t²]     = 8t   So now…

Q: (a f (x) + b g(x)) '= a f (x) + b g'(x)

A:

Q: If f(x) = x'ex, find f'(x) and f'(1).

A:

Q: 7. 8. 9. y = 2 Evaluate the integral x4 6x5 - 1 Evaluate 2 √ (9x² (9x² − 10x + 6)dx Find the area…

A:

Q: The following data shows the height function of a hill a a distance x from a reference. Form a cubic…

A:

Q: Find the Laplace Transform of the following functions

A: Laplace Transform of function cos3t

Q: Use the Euler method to solve the following equation analytically for five iterations. Given that…

A:

Q: A. Find the general equation of the conic with the given properties. A hyperbola with foci at (4-…

A: Given problem:- A. Find the general equation of the conic with the given properties.   A hyperbola…

Q: Write an expression for the function, f(x), with the properties f'(x) = ((ln(x+5))²)/x and f(4) = 3.…

A: We have to find the value of integral.