Does the set of all positive rationals form a group with the multiplication operation? Either verify all of the conditions of the definition, or else show that one condition fails.

Q: Find the general solution of the first-order linear equation dy dx + 2y = e²x

A:

Q: For every solution y(x) of the equation y''+ 2y'+ 5y = 0 it is true that limx→∞ y(x) = 0. ?

A: Consider the equation

Q: Let h(x) = 6x² +1+17x Determine the critical values of h. If multiple such values exist, enter the…

A: Given, .For find critical valuer put h'(x)=0.

Q: The vectors (8, 12, 16) and (6, -9, 12). are parallel. Select one: O True O False -

A:

Q: If 1800 square centimeters of material is available to make a box with a square base and an open…

A: Let the side of the square base = x cmLet height of box = y cm

Q: Estimate the area between the x-axis and the graph of f(x) = 9 - x² over the interval [-2, 1] by…

A: The given curve is The graph given is

Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) =x² + y² subject to the…

A:

Q: Evaluate 3 [[x³y dy dar. Please show 0 decimal places. your answer to 4

A:

Q: 5. Let f(x, y, z) = x²e + ay³ + az + 115. Find fyzz (b) Find 8³1 əxəydy'

A:

Q: Math 152 metric IHU 3. In this problem we'll evaluate the integral cos²(z) sin³ (2) dr. (a) First,…

A:

Q: Find f'(1) if f(x)= x + 1 √x + 1 A

A: we need to find the derivative of function at point x=1.

Q: What values of a and b make the function f continuous everywhere? x² 4 a = f(x) = and b = - " X 2…

A:

Q: Find the length of the arc of the curve-y = (x − 2) = from x = 0 to x = 6

A:

Q: Use partial fraction decomposition to find the following integral -da 24-1

A: I=∫x2x4−1dx

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x²² In(x),…

A:

Q: Suppose a product's revenue function is given by R(q) = -2q² + 700q, where R(q) is in dollars and q…

A: Revenue function is given by:Where, is in dollars is the units sold

Q: What is the minimum degree of the polynomial function whose graph approximates each given graph?…

A: Consider the graph

Q: 11. Identify the horizontal asymptote of * 3 f(x) = +2 x-2 Oy=1 Oy=2 y=3 Oy=-2 Identify the domain…

A: Horizontal asymptote:If  then the line y=L is the horizontal asymptote of the function f(x)

Q: A company that manufactures pet toys calculates that its costs and revenue can be modeled by the…

A:

Q: Find aw/as and aw/ât using the appropriate Chain Rule. Function Values w = y³ - 2x²y x = es, y = et…

A:

Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. 11.…

A:

Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

A:

Q: Evaluate the integral. +C 2x + 9 x² + 6x +34 17 -da

A:

Q: Sketch the level curves of the function corresponding to each value of z. f(x, y) = 4x + 6y; z = -2,…

A: Consider the function

Q: Find the solution of the following problem. y' - (x + y)(x + y +3) = 1

A:

Q: X 3. Verify that f(x)=- satisfies the conditions of the Mean Value Theorem on the closed interval…

A:

Q: 0 1 3 2 X f(x) f'(x) -2 -1 2 N 2 133 When x = 0 then D 1 255 324 X 0 3 g(x) 1 2 g'(x) 2 3 -2 0 g(x)…

A:

Q: Let h(v) = 4v v² +6

A: h(v)=4vv2+6

Q: x2-8x-48 3) lim (2-22x+120. 5) =

A: Given Expression is as follows

Q: y-values 9 8- 7 6 5- * 3 2 1 If f(x) f'(3) = g(x) 1 g(x) h(x) > 2 3 x-values then 4 y-values 4 3 2 1…

A:

Q: (a) Find the differential dy. y = ex/2 dy = (b) Evaluate dy for the given values of x and dx. x = 0,…

A:

Q: TO Find the length of the curve y = In (2 sec x) for 0 ≤x≤ xs 6 The arc length of the curve is (Type…

A:

Q: The magnitude of the vector (3, -2, 4) is 29. Select one: O True O False

A: The given statement "The magnitude of the vector  is "

Q: Find (A) the leading term of the polynomial, (B) the limit as x approaches oo, and (C) the limit as…

A:

Q: (a) Find the unit tangent vector on the curve r(t) = [cos(t),2t, 3sin(4t)] when t = 0. :

A: To find the unit tangent vector on the curve .Note: Since the student has posted multiple questions…

Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

A:

Q: A student solves an optimization problem as in Model 1, except that in the problem Mini and Max are…

A:

Q: 4 Sª 3 16 (x-7)(x + 9) dx

A: I=∫3416(x−7)(x+9)dx

Q: Use the quadratic formula to solve the equation. Give two forms for each solution: an expression…

A: The given quadratic equation is

Q: (a) Find and sketch the domain of the function f(x,y)=√x-1+√y-4

A:

Q: Solve the given initial-value problem. Y(x) = y" + 4y' + 5y = 35e-4x, y(0) = -5, y'(0) = 1

A: y'(0)=1

Q: Question 7 What is a function that could have 4e4 as its derivative? Question Help: Message…

A:

Q: Write an equation for a line perpendicular to y y 4-4 and passing through the point (-8,7)

A:

Q: Evaluate the following integral. A sketch is helpful. R 3 15x² dA; where R is bounded by y = 0, y =…

A: To find:- Where R is bounded by

Q: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros: 1;…

A: Form a polynomial f(x) with real coefficients having the given degree and zeros.Degree 5 ; zeros: 1…

Q: 4. Use Calculus to graph g(x)=x² + 4x³. Make sure that your graph shows all intercepts, extrema, and…

A:

Q: If u and v are the vectors below, solve the following equation for the vector x. 2 4 u= -1 v=|–1 5…

A:

Q: Suppose that in a certain biology lab experiment, the number of bacteria is related to the…

A: Suppose that in a certain biology lab experiment, the number of bacteria is related to the…

Q: Consider h(z): 2 5 - Oh is concave down on: Oh is concave down nowhere. 1 2 Determine the intervals…

A: Consider the function To determine the intervals on which  is concave up and concave down.To…

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4 + x² -…

A: