x-axis. x = find the area of the surface obtained by rotating the curve about the 1 (y² + 2)³/², 1 ≤ y ≤ 2

Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

A: The Laplace transform is a mathematical tool used to transform a function of time, typically a…

Q: Find the 102nd term of: -8, -14, -20, ....

A: Solution

Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y=3x,…

A: The equation of line segment y=13x,0≤x≤7 Graph

Q: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros:…

A: Degree of the polynomial is 4, zeros are 2-2i and 5 multiplicity 2. Since complex roots occur in…

Q: Find the length of the equiangular spiral r = (Use symbolic notation and fractions where needed.) 5e…

A: To find the length of the equiangular spiral r=5eθ for 0≤θ≤2π.

Q: 225 Find the equation for the tangent line to f(x) = I at the point (5, 45).

A: given function f(x)=225x

Q: For the function f(x) = 3x²e²x find the points where the tangent to the curve is horizontal.

A: This is question of calculus  here function is given  we have to find tangent of horizon  further…

Q: A box with must open top 62, 500 cm³, find in 2m thord box material Sides of height: used base :…

A: A square base box Volume= 62500 cm3  We have to minimize surface area so that material used can be…

Q: 6. Solve the initial value problem for x as a function of t.. dx (1²-9t+20)=1 for (t> 5), x(6)=0 dt…

A: we have given differential equation t2-9t+20dxdt=1, x(6)=0

Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the…

A:

Q: x²-16 3 A) -4 and 4 and- 2 C) -4 and 4 B) 4 D) Nonede D) a 10)

A:

Q: The four sequential sides of a quadrilateral have lengths a = 5.2, b = 8.4, c = 10.8, and d = 12.4…

A:

Q: Find the indefinite integral using the substitution x = 3 sin(0). (Remember to use absolute values…

A: The given integral is: ∫9-x2x dx

Q: The plane through the origin and the points (2, −4, 8) and (8, 4, 4)

A:

Q: Find the length of spiral x=40² 2 48 03826 Lev. 40² 2 ² + (²) ² de

A: r = 4θ2Length = L L = ∫ab[ r2 +( r' )2]dθ0 ≤ θ ≤ 6

Q: Q7 Given f(x) = 5-6x² + x³. How many critical numbers could f(x) have? (a) 0 (b) 1 (c) 2 (d) 3

A:

Q: K Solve the initial value problem below using the method of Laplace transforms. 3t y' + 6y' + 5y =…

A: y"+6y'+5y=160e3t, y(0)=-5,y'(0)=49

Q: Find h'(t) given:h(t) = - 4.9t2

A:

Q: Graph the feasible region for the system of inequalities. Tell whether the region is bounded or…

A:

Q: Find the scalar and vector projections of b onto a. a=3i-j+4k, b=j+k

A:

Q: Find the average value gave of the function g on the given interval. 8 1+ t²' gave = g(t) = [0, 9]

A: The function isgt=81+t2 ; 0,9

Q: Find the solution of the differential equation that satisfies the given initial condition. dy dx =…

A:

Q: Solve the inequality algebraically. 3x³> -12x² List the intervals and sign in each interval.…

A: Solve the inequality

Q: Enter if the sequence below is: Arithmetic, Geometric, or Neither: -5√5,25,-25√5,... Enter the next…

A:

Q: Which of the following does not provide the exact value of the instantaneous rate of change at x=a?…

A: The instantaneous rate of change of a function f(x) at a point x=a is the derivative of the function…

Q: The expression 729g¹y³√729g4y³ = kg"y where:

A:

Q: (1) (2) Find the points on the curve where you have a horizontal tangent line for the function…

A:

Q: 13) Given f(x) = x − 3x Analytically [using calculus] determine the following for the function f.…

A: We can solve the given problem by using the first derivative test

Q: Find the complex zeros of the quadratic function. Graph the function. f(x)=50x² +10x+1 (Simplify…

A: To find the complex zeros of the quadratic function. To graph the function. fx=50x2+10x+1

Q: Use the graph of the function f to solve the inequality. (a) f(x) > 0 (b) f(x) ≤0 (a) The solution…

A:

Q: ind the vertical, horizontal, and oblique asymptotes, if any, for the given rational function. x-16…

A: Find the vertical, horizontal, and oblique asymptotes.  G(x)= x4-16x2-2x

Q: For the line through (,) and (-1,3), find the parametrization of y(t) if x(t) = 1/-3/t. (Use…

A:

Q: Find sin(0); if sec (0) = 2, with 0 in quadrant IV. Give a reduced answer in exact form. sin (0) =

A:

Q: Could you please resolve this and make it handwritten for me to better understand. im not sure if…

A:

Q: Graph  f(x) = ax  for  a =  1 3,   a = 1,  and  a = 3,  all on the same set of axes.

A: Given: f(x)=ax We are required to: Draw the graph of the given function for a=13,a=1 and a=3.

Q: Find the derivative of the function. f(x) = sin(x² + 5)

A: given f(x)=sin(x2+5)

Q: Consider the following. [²3 dt = Let t = 7 tan(0) and determine the following. 1) de t = 0 → 0 = dt…

A: To find out the integration.

Q: 2 a&b) Evaluate : "sin²x cos*x dx. If f f(x) dx = 10 and ſo f(x) dx = 7, find ſo f(x) dx.

A:

Q: 5. Determine, with justification, if [1,3,2], [4,0,1] and [-2,6,3] are coplanar. [3 A]

A:

Q: Find the second derivative of the function. f(x) = In(x + 3) f"(x) =

A:

Q: Find the indicated limit, if it exists. (If an answer does not exist, enter DNE.) lim (4x²+2x+10)…

A:

Q: You're trying to save to buy a new $194,000 BMW 3 series sedan. You have $44,000 today that can be…

A:

Q: Using the Method of Undetermined Coefficients, determine the form of a particular solution for the…

A:

Q: Write the function whose graph is the graph of y=√x, but is shifted to the right 2 units. y=…

A: To write the function whose graph is the the graph of y=x, but is shifted to the  right 2 units.

Q: Evaluate the integral. (Use C for the constant of integration.) | 8 sin²(x) cos³(x) dx

A: The integral is ∫8 sin2xcos3xdx

Q: cep and indicate where tables were used in a step. No points will be given fo riting the answer. 2y"…

A:

Q: A semicircle of radius r=4x is inscribed in a rectangle so that the diameter of the semicircle is…

A: The radius of the semicircle is given by 4x To express the area of the rectangle in terms of x and…

Q: a) A company estimates their total cost, in dollars, to be C(x) = 38000+ 6x +10√ when they produce z…

A: Given : Total cost, in dollars, to be C(x) = 38000+6x+10√x when they produce x items.  Find the…

Q: Find all the values of a such that the given series would converge. 3)" n( − 9)" n=1 The series is…

A: The given series is ∑n=0∞(x-3)nn(-9)n.

Q: Find the first and second derivatives of the function. f'(x) f"(x) = L √7x - 6

A: