Which of the following DE has separable variables? O (xy? + x)dx + (x²y-y)dy=D0 O (x- y)dx+(3x+ y)dy=0 O (x³ + xy2 + x?)dx + x²ydy=D0 O 2yly? – x)dy = dx

Q: y = xx, x 4, and y = 0 Revolve the area of the shaded region about the x-axis. Using circular disk…

A:

Q: P6: x2 dx x² – -2

A: We will use substitution method to solve the integral.

Q: dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the…

A:

Q: Match each graph type with its corresponding function. 1X Linear Function 1 y%3 2 2. y= log1 X…

A:

Q: Explain why the function f(x) = ez is not injective (one-to-one) on its natural domain.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 10. By trigonometric substitution, we can transform dx into x*V4 - x2 A. Ssi'e sin ede В. 1 1 С. 32J…

A:

Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

A:

Q: If f(x) = (x2 + 5x + 8)*, then f'(x) = f'(5) =

A:

Q: 3. If f(x) = [ 8+f dt ,find f'(1). .

A:

Q: 2. Write the given (total) area as an integral. a. The area above the x – axis and below y = 4 – x2…

A: Let's find.

Q: 2х +1 f(x) = 4х-2 е.

A:

Q: The junior class has 50 students. Fifteen students take only French, 5 students take only Latin, and…

A:

Q: 3. Write z = 12.2 - 31 in polar form. Use 3 decimal places.

A: The objective of the question is converting to polar form.

Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

A:

Q: Use the figure to evaluate the following function, given that h(x) = tan x. (Simplify your answer.…

A: This question can be solved using the concept of trigonometry.

Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

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: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx. Write the given…

A: To find out the value of integral using the midpoint rule.

Q: dy 15. Vx eu+ Vx, dx x > 0

A: We have to solve the difference equations

Q: 5. For vectors given the vectors v =(-4,-3) and w (-1,-1), find: (a) Sketch, v+w below. Find its…

A: We can solve as follows

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: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

A:

Q: 1 is convergent or 8. 1) Use the Comparison Test to determine whether the series n=2 divergent. Show…

A: We need to find if series is convergent or divergent,

Q: sin ® 3y cos3ydy cos 3y dy

A: We have to find out the integral

Q: 3n° + 2n³ - 7 {a,}== 7n' + 3п +4

A:

Q: Determine the area of the given region. y = x + sin x y 4 3

A:

Q: 2. Find the particular solution to the differential equation dy 2y? dx cosec (x) if the point…

A:

Q: Find the equation of the tangent line to y=(3x+4)3 at the point where x= -2

A: here given y= (3x+4)3 slope  of the tangent line is y'    Here y' = 9(3x+4)²   Value of y at x=-2 is…

Q: solve with complete solution, tell whether the improper integral is convergent or divergent

A: Yes the improper integral is convergent. see below the answer and calculation

Q: Find the derivative of the following:

A: The given functions are:a. fx=3x+tan2xb. y=cos32x.We need to find the derivative of the above…

Q: 5) Find the unit vector in the direction of v = 2i + j+k 1 - i+-j+ d) i+j+k 1 1 j+ V5 а) V5 k b)

A: We can solve this as follows:

Q: Use the chain rule to find the derivative of f(x) = 6/3x + 5x10 Type your answer without fractional…

A:

Q: ind all the relative extrema and saddle points, if any, of the given function below: f (x, y) = ln(x…

A: Relative extrema and saddle points: Consider the function f(x,y)For critical points , fx(x,y) = 0…

Q: 14. Write the solution set for the general solution. Write the solution set on the interval [0, 2n).…

A:

Q: f(x)=/1+2sin x j. f(x)=e" +4* +sinh(10x)

A:

Q: 4. The complex numbers u and v are as follows: u = 3cis(1.234) and v = 2cis(2.415). Write the…

A:

Q: 1) Use the Integral Test to determine whether the series > 1 is convergent or divergent. n=1 (3n–…

A:

Q: Find V. (V x F) if F(x, y, z) = 4 sin xi + 5 cos(9x – 10y)j+ 10zk. V·(V × F) =

A: topic- vector field

Q: dx 2. To evaluate | by trigonometric substitution, we let (5 – 4x – x - A. x+2= 3tane B. x+2= 3sine…

A:

Q: The probability that an event will happen is . What is the probability that the event will not…

A:

Q: The demand for grass seed (in thousands of pounds) at price p dollars is given by the following…

A: The demand for grass seed in thousands of pounds at price p dollars is given by the following…

Q: 6. Compute and write the slope of the tangent lines to dx y - xy +6 = 0 at the point (5,2). a. b. 2y…

A:

Q: y = x and y =x+2 ve the area about the line x = 3. Using cylindrical shell method, the volume of the…

A:

Q: d d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt dt the product directly…

A:

Q: Find the exact value of each of the following trigonometric functions of 0. 12 90° <0<180° 13 sin 0…

A: Given:-sinθ=1213,        90°&lt;θ&lt;180°

Q: 20. The length of a rectangle is increasing at a rate of 5 cm/sec and the width is decreasing at a…

A:

Q: X = -y A y 2Fx = 2- y² -2

A: Recall: Formula Area=∫abf(y)-g(y)dy  We have,  f(y)=2-y2, g(y)=-y

Q: Show that the function f defined by 1. (x, y) = (1, –1) f (x, y) : x² + y .2 (x, y) + (1, –1) x + Y…

A:

Q: long

A: We will use long division method.

Q: IV. Suppose z is a function of r and y, and tan Vy² + x² 2e&y¸ Solve for az az and dy

A: Since the student has posted multiple questions and does not mention any specific question, so we…