Solve the differential equation (2x + y) dx (4x + 2y − 1) dy = 0 O a. 5x 10y + In 10x 5y 2|= C O b. 5x 10y + In |10x + 5y - 2| = C O c. 5x+10y + ln |10x 5y - 2|= C O d. 5x+10y + ln |10x + 5y - 2| = C -

Q: Let f(x) x³ + 6x² 36x +11. = (a) Use the definition of a derivative or the derivative rules to find…

A:

Q: = Approximate the area under the curve y = x² from x with 6 subdivisions. 3 to 6 using a Right…

A: We have to approximate the area under the curve using Right Endpoint Approximation.

Q: 2 -1 4 3 N у -1 1 2 X

A: Graph of the function is given, we have to find its domain and range

Q: 04115

A:

Q: For the linear function y = f(x) df dx a. Find at x = 8. ƒ'(8) = b. Find a formula for x = f-1(y).…

A:

Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…

A:

Q: Find the length of the Arc length= curve r(t) = (71, 5, √¹4²) for -4 ≤ t ≤ 4. 2

A:

Q: f(x) = = -2x² + 7 7x - 10 if x -1

A:

Q: The volume of the box is 54 cubic inches. The material for the top cost $0.08 per square inch, for…

A:

Q: A manufacturer can produce 4320 cell phones when a dollars is spent on labor and y dollars is spent…

A:

Q: Find the area under the curve y 7 x over the interval [1, 5]

A: Given curve y=7x

Q: Find F as a function of x and evaluate it at x = 0, x = 7/3, and x = 7T/2. F(x) = F(x) = F(0) = (7)…

A:

Q: Consider the function f(x) = 1-5x², -4≤ x ≤ 1. The absolute maximum value is and this occurs at x =…

A: Consider the function fx=1-5x2, -4≤x≤1.To determine absolute maximum and absolute minimum value of…

Q: 1. The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in…

A:

Q: 4) Find the equation of the line tangent to h(x) = (2-x)(x³ +4x-4) at x=1.

A:

Q: The graph of g' is given below: W Notice this is the graph of the derivative of g not the graph of g…

A: Given graph of g' is shown below

Q: Write the interval in set notation. [2, 6) {x | 2 < x ≤ 6} {x | 2 ≤ x < 6}   {x | 2 ≤ x ≤ 6} {x | 2…

A: Write the interval in set notation. [2, 6) {x | 2 &lt; x ≤ 6} {x | 2 ≤ x &lt; 6}   {x | 2 ≤ x ≤ 6}…

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: Given that f(x)= e3x (8-x) . We find intercept point and relative maxima and minima and point of…

Q: Question 4 Use Laplace transforms to solve the differential equation: d²x di 2 + 4x = cos(21) where…

A: Topic:- application of integration and differential equations

Q: Please show me how to find the x value.

A:

Q: Calculate: fx²e³dx

A:

Q: (−4 − x)² +5 if x ‡ − 5 Let f(x) 4x + 25 if x = -5 Calculate the following limits. Enter "DNE" if…

A:

Q: Use a system of linear equations with two variables and two equations to solve. A number is 8 more…

A:

Q: 13. A radioactive isotope has half-life of 43 days. What percent of the original amount remains…

A: Topic:- application of algebra

Q: Evaluate ſ F . n dS if F = (x + y² ™)ī − (2x)j + (2yz)k and $ is the surface of the plane 2x + y +…

A:

Q: Consider the function f(x) = 4 − 2x² on the interval [ – 2, 3]. Find the average or mean slope of…

A:

Q: 4 sin(x - 2) x→2 3 ln (3x – 5) Evaluate lim and write your answer in simplest form.

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

Q: 12. Given the vector equation [x, y]= [3,1]+[3,-5] find a) the parametric equations b) the symmetric…

A:

Q: Find the slope of the tangent line to the curve − 3x² – 1xy – 3y³ = at the point (-2, − 1). 11

A:

Q: -10 -5 f(x) 10 10 5 10

A: Note: Since the student has posted 2 sub-parts of the question in which the part (1) is complete and…

Q: Solve x (az + √2) dx y (az + √2) sin (ay²) dy + (az − √2) dz = 0 4√/2ln |az + √2 = C 4√/2ln|az +…

A:

Q: Determine whether the function is differentiable, continuous, both, or neither at the value where…

A:

Q: Find F as a function of x and evaluate it at x = 0, x = 7/4, and x = 7/2. 1-² sin € F(x) = F(0) =…

A:

Q: Find all local extreme values of f(x) = - The FIRST local extreme value, moving from left to right…

A: Topic:- application of derivatives

Q: For an object in an elliptical orbit around the moon, the points in the orbit that are closest to…

A:

Q: Find the equation of y, given the derivative and the indicated point on the curve. dy dx = 2x - 1 y…

A:

Q: 1. Carbon 14 is a common form of carbon which decays over time. The initial amount of carbon 14…

A: Please see the below pictures for detailed solution.

Q: Find the unit tangent vector T(t) for r(t) = 4ti + 7t²j + 3tk. T(t) =

A:

Q: 3. A particle moves along the x-axis with velocity v(t) = t2-1, with t measured in seconds and v(t)…

A: Given velocity v(t)=t2-1 To get the total distance traveled, we have to integrate the velocity…

Q: 3 -2 7 4 3 2 1 -1 2 3 X

A:

Q: 2. (xy + x) dx = (x²y² + x² + y² + 1)dy

A:

Q: 2. 3. (32²+7)dx=(2,₁¹²₁ )dy = 0 4) 1 xe²x dx + (5-1)dy = 0, y(0) = 0 1

A:

Q: = $r(t)dt 5. Use the graph of f(t) = 2t - 5 on the interval [-2, 10] to write the function F(x),…

A:

Q: Find the length of the given curve: where -4 < t ≤1. r(t) = (-2t, 2 sin t, 2 cos t)

A:

Q: Find the the e following: sinx first maclaurin four Series nonzero for terms of each (21) S² Tara d…

A:

Q: 6)Find the first quadrant area of the region bounded by curves defined by given equations

A:

Q: y-e-x4cos4x ស

A:

Q: Consider the function f(x) x² + 7x + 12 2-5 a. Find the first derivative. f'(x) = b. List any…

A: Solution is here

Q: 00 ΣΤΑ 1 — (−1)n-¹n² 10 Select one: O True O False ≈ 0.0676

A:

Q: Find the area under the curve y 9 x over the interval [1, 5]

A: