If f(x) = 4x² − 4x + 2, find f'( − 3). Use this to find the equation of the tangent line to the parabola y = 4x² - 4x + 2 where x = -3. The equation of this tangent line is |

Q: Question eleven: We suppose that {1,2,3,4} = A that f: A→ A is a defined function as in the…

A: Given Data: Set A=1,2,3,4 Function f: A→A

Q: The curvature of a plane parametric curve x = f(t), y = g(t) is given by |x y - yx| [x² + y2]3/2…

A:

Q: x² - 10x (c) lim 9x²-x 2

A: L’Hospital’s Rule Formula L’hospital’s rule states that Note: The limit of the quotient of function…

Q: 6. y = x² + 4x; x dy dx = x² + y

A: NOTE: As per our guidelines, I have solved one problem. If you want solutions of rest, kindly post…

Q: N 2 -3 EXAMPLE 5 Find an equation of the tangent line to the parabola y=x²-8x + 9 at the point (2,…

A:

Q: Simplify the following expression [8t¹9 — 9t¹4 + 7t − (−6t¹9 + 77¹4 − 8t)] − [−8+¹9 − 10t¹4 + 7t +…

A:

Q: 3) If x³ ≤ f(x) ≤ x for x in [-1,1], find lim f(x) if it exists. x-0

A:

Q: Find the solution of the differential equation y(t) = = 1 t sec y = 6 cos t { x + + + ² ( 1 ) x - *…

A: The given differential equation is  y'+1/5sec(t/5) y= 6cos(t/5) , y(0) = 1  where 0<t/5<

Q: Use PMT= P == -nt to determine the regular payment amount, rounded to the nearest dollar. The price…

A:

Q: h (s, t) = t²ln(s²) + √√SA

A:

Q: 73. lim sin 3t t⇒0 2t

A:

Q: Laplace (d^2y/dt^2) + 6(dy/dt) + 9y = cost y(0)=1, y’(0)=2 What is Y(s) and y(t)

A: We know the following. L{y''}=s2Y-sy(0)-y'(0)L{y'}=sY-Y(0)L{y}=Y Now,              y''+6y'+9y=cos t,…

Q: 9. Find the area bounded by y = x², y = -x, from x = 0 and x = 2. A. 2/3 square units B. 8/3 square…

A: As per our guidelines we are allowed to solve only one complete question. kindly repost others.…

Q: nd the average value of the function f(x)=48-12x² over the interval -5≤x ) 1) -152 2) -52 3) 148 4)…

A:

Q: III. Eliminate the arbitrary constants of y = c₁ cos3x + c₂sin3x.

A: Given function, y=C1cos(3x)+C2sin(3x)

Q: Use the indicated substitution to evaluate the integral. 17/2 rdz 289 17/2 1. x = 17 sin t x²dx √289…

A: To evaluate the given integral.

Q: Problem 1. integrals. Suppose you know that the following integrals. (a) √ [²ƒ(t) + 3] (b) √² 3f (t)…

A:

Q: Suppose that f(x) is a continuous function over all real numbers, f'(-16)=0, and f''(-16)=27 Which…

A: Given fx is a continuous function, f'-16=0 and f"-16=27

Q: a.) √ 1 csc² x+sec² x cosx-cos³x - dx

A:

Q: On what interval is f(x)=x²-16x +17 decreasing? Enter INF for infinity or -INF for negative…

A:

Q: 1) The volume of a right cylinder is given by the equation V = r² h, where r is the radius and h is…

A:

Q: Simplify the following expression. 3x 15 + 10y X 5y5 5 10y + 5 5y³ ...

A:

Q: FORMATTING: Write your answer in the form [p(x), q(x), r(x)], including square brackets and commas…

A:

Q: Question 13: We suppose that {A = {a, b, c, d and {B = x, y, z, w. What is the function between…

A:

Q: x²yy' = e'.

A:

Q: y= Cix2 + Cze' C₂e² 2X

A:

Q: Find equations of the lines that pass through the given point and are parallel to and perpendicular…

A: The given equation and point is; 3x+4y=7, (-2/3, 7/8).

Q: Given f(x) = -2x² - 2x + 4 x-1 1 which of the following statements are true? Select the correct…

A: A function f(x) is continuous at x=a if and only if limx→a f(x) =f(a) .

Q: 2 X² +4X-9 = 0 Solution Set {} 3

A:

Q: Let the position vector be R(t)=⟨3t,4cos(3t),4sin(3t)⟩. Compute the principal unit normal vector…

A: Given data:- The given position vector is, Rt=3t, 4cos3t, 4sin3t

Q: Researchers measured the average blood alcohol concentration C(t) of eight men starting one hour…

A:

Q: If y = sin(x - y) find y'. A. cos(x-y) 1+cos(x-y) B. cos(x-y) 1-cos(x-y) C. cos(x - y) D. -cos(x -…

A:

Q: A disk-shaped piece of fruit has a volume gicen by V=3.1², where r is the radius and V is the…

A:

Q: Find the domain of the following function. Give your answer in interval notation. Provide your…

A: Given query is to find the domain of the function.

Q: ef= dx e + e- Evaluate

A: To evaluate the following integral.∫dxex+e-x

Q: Determine the solution of the 1st Ordered Differential Equation: y(x² + y²)dx + x(3x² - 5y²)dy = 0

A: y(x2+y2)dx+x(3x2-5y2)dy=0x(3x2-5y2)dy=-y(x2+y2)dxdydx=-y(x2+y2)x(3x2-5y2) Substituting  y=vxy'=v'x+v…

Q: An object is dropped from the top of a 100m high tower. Its height above the ground after t sec is…

A:

Q: Find the positive root for x^2 - 0.9 x -1.52 0 = in the interval (1, 2) by the Bisection Method with…

A: The given equation is; x2-0.9x-1.52=0.

Q: DO THE FOLLOWING: 1) COPY AND EXPAND (ADD NECESSARY INFORMATION TO MAKE THE SOLUTION BETTER)  2)…

A: We have to give a model of real-life phenomenon in physics using rational functions.

Q: Solvex -3x 256x-2x Express your answer in interval notation:

A:

Q: 1. Let z = f(x, y) = -tan x + y² + eysin. (a) Use local linear approximation to approximate the…

A:

Q: . Find the volume of the solid generated if the area bounded by y=x², x=2, ar x-axis. A. 32/5 cubic…

A:

Q: I. Find the general solution of each of the following. 1. xy²dx - edy 2. tanxdx+ycos’ xdy−0 3. ytan²…

A:

Q: Let the velocity vector be v(t)=⟨5t^4,−3sin(t),4exp(2t)⟩ and the initial position vector be…

A:

Q: Find the domain of the following function. Give your answer in interval notation. Provide your…

A:

Q: 2 2 Find for x² + y dy dx 2 = a³

A:

Q: The range of y = tan-¹ x is A. R Evaluate lim h-0 A. undefined B. [-1,1] (x-h)³-x³ h B. 3x² C. x +…

A:

Q: Differentiate the function.

A: y=3ex+8x3 Differentiating with respect to x…

Q: Minimum value of x?

A: The given graph is:

Q: 4 9 Find the critical points of the function f(x) = 45x 5 + x 5. Enter your answers in increasing…

A: