Use Laplace transforms to solve the initial value problem: y" - 4y = 2e³t, y(0) = 1, y'(0) = −1

Q: Find the Taylor polynomials p1​, ​..., p5 centered at a=0 for f​(x)=4e^−2x.

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min.…

A:

Q: [ sin* .rd.

A: ∫sin3x dx=?

Q: Let f(x,y) = (- (2x+y))'. Then 02f дхду 83f Әхдудх 83f дх2ду

A: Explanation of the answer is as follows…

Q: 3. Let f(x) = 2x - x². (a) Find the secant line to the graph of f passing through the points (0,0)…

A: We can find equation of secant line and tangent line .

Q: Question 1. equation : y cost + 2te³ + (sin t + t²e³ − 1)y' = 0. 1: Consider the differential a)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Question Find the Taylor polynomial p2(x) for f(x) Provide your answer below: p₂(x) = 6e² at x = 1.

A:

Q: 4 Evaluate the integral. [*¹²5√1-cos40 de

A:

Q: Consider the function g given by g(x)=|x−6| +2.   ​(a) For what​ x-value(s) is the function not​…

A: A function is non-differentiable when there is a cusp or a corner point in its graph.   Given :…

Q: Find the point on the curve r(t) = (5 sin t)i + (-5 cos t)j-12tk at a distance 26 units along the…

A:

Q: box is to have a square base, no top and a volume of 108 cubic centimeters. What is the smallest…

A: We have to find the total surface area of a box , whose base is square and no top . Therefore total…

Q: (1) If f(x) = = x², then f'(x)= (3) If h(x) (2) If g(x) = - 6x5, then g'(x) = = 1 = I then h'(x) =

A: formula used is   dxndx=nxn-1d dx(constant)=0

Q: An expression for which the derivative is v² +6v is v³ + 3v² That is, v³+3v² is an antiderivative of…

A: We have to solve

Q: List the first five terms of the sequence. an+1 = 2an + 6 a1 a2 a3 24 a5 = = a₁ = 3₁ 3,

A:

Q: Draw the angle in standard position. State the quadrant in which the angle lies. Work the exercise…

A: Given : 11π6

Q: If a cup of coffee has temperature 96°C in a room where the ambient air temperature is 19°C, then,…

A: Find average temperature of first 20 minutes.

Q: nd the equation of the tangent line to the curve y = at the point (5, 10). The equation of this…

A:

Q: (a) Complete the square by writing 2 - 12x - 19 in the form (x-h)2 + k. Note: the numbers h and k…

A:

Q: If ​f(x)= 2x2 −5x+3​, find f′(3).

A: To find f'(3)

Q: (x) x + 1/2 Ax² + Bx + C (x² + D)²

A: Topic:- application of derivatives

Q: Evaluate the limit 3 + 3x² (11+52)

A:

Q: A ladder 10 ft long rests again a vertical wall. If the bottom of the ladder slides away from the…

A: We can solve the given problem by using the concept of derivatives.

Q: write the exponential funcetion y=50(1.025)^t in the form of y+a(e)^kt, indicate whether the…

A:

Q: Find dy/dx. y=x-4

A:

Q: Find the partial derivatives of the function fz(x, y) fy(x, y) fay(x, y) fyr (x, y) = f(x, y) =…

A:

Q: A box with no top is built by taking a 6-inch-by-6-inch piece of cardboard, cutting ?- inch squares…

A:

Q: Find the inverse o a. f(x)=2x²-4

A: according to bartleby guide line we do only first of multipy.a)  f(x)=2x2-4steps for finding inverse…

Q: Find the second derivative of the function. f(x) = x In(√x) + f"(x)= = + 6x

A:

Q: The DE M(x,y) dx + (3e-4x + 7y)dy=0 is an exact differential equation if O M(x,y)=-12ye-4x - 8y O…

A:

Q: city of Pittsburgh. The Revenue function R(q) for the program was given by: -0.00381q² + 62.476q 100…

A: Formula for average rate of change

Q: (7 y² +6 x)dx+ 11 x y dy=0 (*) a) Determine whether the given differential equation (*) is exact…

A: We have to determine whether the given differential equation (*) is exact

Q: Find the coordinates of the point (x, y, z) on the plane z = 2 x + 3y + 2 which is closest to the…

A:

Q: Given s(t)=3t2+12t​, where​ s(t) is in feet and t is in​ seconds, find each of the following. ​a)​…

A:

Q: Let f(x) ƒ'(0) = 5e +2 +e-¹.

A:

Q: find it's derivative and solve for its critical points

A:

Q: Question Differentiate the series represented by the function f below term-by-term to find the power…

A:

Q: The function f(x) 2√√x + x³ - has a x² +√√x + 3x Horizontal Asymptote at y =

A:

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A: Given query is to find the rate of change of base.

Q: 11. INSTRUCTIONS: Two cars start moving from the same point. One travels south at 60 miles per hour.…

A: Given

Q: дz 3. Given xyz = z + sin(x+y), find Әх

A:

Q: Find the critical numbers h(x) = (x-1) / (x2 + 4) *please use handwriting not typing, I understand…

A: Given query is to find critical points

Q: Use a definite integral to find the area under the curve between the given x-values. f(x) = x² from…

A:

Q: b) The cost structure for iPhones are as follows, fixed cost of $25 and variable cost per unit of…

A: Given:Fixed cost=$25Cost price per unit=$2

Q: INSTRUCTIONS: Differentiate with respect to g(x) = ln(x√x² - 1)

A: according to bartleby guideline we do only first part g(x)=lnxx2-1d…

Q: This question reviews the process for integrating definite integrals using u- substitution and…

A: use the substitution method for finding the integral.

Q: compute log(0.01)

A: Find the value of indicated logarithmic expression.

Q: The position of a particle moving along a coordinate line is s=root 28+4t​, with s in meters and t…

A:

Q: he concentration of a drug t hours after being injected is given by C(t)=0.5t t^2+59. Find the time…

A: Topic:- application of derivatives

Q: If f(x, y, z) = xe² sin (42), then the gradient is Vf(x, y, z) =

A:

Q: Evaluate the integral f(2x- (2x + 8) (x² + 8x + 6)¹ dx by making the substitution u = x² + 8x + 6. +…

A: