Q5.Solve the following ODE problem using Laplace: a- ÿ − 6ỷ + 13y = 0, where y(0) = 0 and y(0) = -3 b- x - 2x + 3x = f(t), where x(0) = 0, x(0) = 4 and f(t) is represented by the following graph: f(t) t 4 3 2 1 0 -1 -2 -3 0 0.5 1 1.5 2 2.5 3 3.5 t 4

Q: 12) Consider the following function 9: R R q(t)= |t(t - 8) (t – 5)|. If m is slope of the tangent of…

A: Given that, q:ℝ→ℝ and q(t)=|t(t-8)(t-5)|. m is the slope of the tangent of the function q(t) at…

Q: The equation of the tangent line for the function f(x) = -7 – 5x at z = 7 is O y = -5(1 – 7)+42 O y…

A:

Q: 1. Determine the particular solutions of the following function. (D3 – 3D – 2)y = 0; when x = 0, y =…

A:

Q: Give a function that does not have an inflection point at a pointwhere f ″(x) = 0.

A: Example  f(x)=x4

Q: Find y as a function of x if X y(0) = −1, y′(0) = 9, y″(0) y(x) = = -16. = y" - 4y" y + 4y = 0,

A:

Q: 4. The acceleration of a particle is modeled by the function a(t) = t³ – 61² – 37t – 30 where t is…

A: Please see the answer below.

Q: Find the indicated value of the function f(x.y.z) = 3x - 5y? + 9z° - 6. f(9, – 3,1) f(9, - 3,1) = O

A: f(x,y,z)=3x-5y2+9z3-6f(9,-3,1)=3×9-5×((-3)2)+9(13)-6f(9,-3,1)=27-45+9-6f(9,-3,1)=36-51f(9,-3,1)=-15

Q: Find the equation of the tangent to the curve at x = 3 for the function: f(x) = [(2x+1)³ (4x-3)

A:

Q: 11. Find a standard Cartesian equation for the line that is tangent to the curve F(t) = (2+) at the…

A:

Q: 4. The position of an fictitious particle moving in a straight line, in metres, is described by the…

A:

Q: Find y as a function of x if y(0) = 10, y(0) = 10, y"(0) = 18. y" - 16y" +63y = 144e",

A:

Q: "; Find y as a function of x if x?y" + 5æy' – 21y = x°, y(1) = 7, y(1) = -5. y =

A:

Q: The equation of the line tangent to f(x) = (x² – 9) (2x – 1) at æ = 2 is y = 2x –*

A: Given that: f(x)=(x2-9)(2x-1)

Q: L. Let h (x) = f (x) g (x). Find a. h' (1), b. h' (3), and с. h' (4).

A: According to the given information,

Q: Find an equation for the line tangent to the graph of 3x + 2 f(x)=2x-1 at the point P(1, fƒ(1)). 2 y…

A: f(x)=3x+22x-1point(1,f(1))f(1)=3+22-1=5point is  P(1,5)eqation of tangent line is  y=mx+c where m is…

Q: (a) Note that (-1,0) lies on the curve x? + y² = 1. For t e R, denote by le the line with slope t…

A: (a) The line lt intersects with (-1, 0) and (x(t), y(t)).  Look at the following image. We know two…

Q: The equation of the tangent line for the function f(x) = -7 – 7x at æ = 5 is

A: Given,  f(x) = -7-7x Slope of function, m = f'(x) = -7 Now,  f(5) = -7-35 = -42 ∴ y = -42 for x = 5…

Q: 2. The acceleration e²t - 25 of a particle at time t > 0 is given by a(t) + 2. Given that the…

A:

Q: 1. The curve y = x? – ax + b has turning point (1, 3). Find a and b.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 4. Find and classify the stationary points of each of the following functions: (a) f(x, y) = x³ +…

A:

Q: a. Give an e Then, de

A: Horizontal shift:The equation indicating a horizontal shift to the left is y = f(x + a). The…

Q: Differentiate the following functions: Chain Rule

A: NOTE: Refresh your page if you can't see any equations. . take derivative apply chain rule

Q: Find the solution of the following linear ODE given that y(5)=3 dy Зу = (x – 4)² х—4 dx

A: Use integrating factor for the differential equation.

Q: 1 (d) Last week, Amy walked a median of 7.5 kilometres each day. 1 kilometre = 0.6 miles The table…

A: