A function f(1) is given by f(1) = h + ab' and has the properties: • f(t) has a horizontal asymptote at y = 3. • f(1) passes through the points (0, 11) and (3,4). Find the values of a, b, and h: h =

Q: Find y as a function of a if y(0) = 7, y'(0) = 4, y"(0) = 133. y(x) = y" - 8y" -y + 8y = 0,

A:

Q: What curve is described by the function (t) = (2t + 3) + i(t - 5), 0 ≤ t ≤ 1

A: Step:-1 Given parametric function is ft =2t +3 +i t-5,  0≤t≤1 Here,  x=2t +3  ---(1)y=t-5  ---(2)…

Q: graph of (x) = x' - 2 is shown in the figure. Find 6 such that if0 2 ]x - 4] 2 8, then IAX) - A. ô =…

A:

Q: Find y as a function of a if y(1) = 3, y'(1) = -7. y = r²y" + 3xy' - 63y = 0,

A:

Q: Use the graph of f and g. Let p(x) = f(x)g(x) and g(x) 2 (a) Find p'(4). p'(4) = = (b) Find q'(1).…

A:

Q: Consider the function f(x) = 4x − x² and the point P(1, 3) on the graph of f. (a) Graph fand the…

A:

Q: The curve y = f (x) passes through the point A(1; 2). Each tangent at any point M(x,y) on the curve…

A:

Q: 3. (a) For P(t) = (4t² + 3) (2t³ — t)¹², find P'(t). After taking the derivative(s), do not simplify…

A:

Q: L=2-36X, y'co) =5, and ylo)=S x)

A:

Q: a) Differentiate the function Q(p) = -2√/p³ (e-P-PB). b) Hence or otherwise, determine Q'(1).

A: The given function .The aim is to find the derivative function  and find the value of .

Q: Which point on the curve y = √x - 4+9 is closest to the point (7, 9)? (x, y) = ( What is this…

A:

Q: f(x) = xª -4 and Perpendicular to the line x - 4y + 1= 0.

A:

Q: Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

A: We can represent all the points on the curveg(x) = x2-2 as (x, x2-2)Now we will use the distance…

Q: Assume that ƒ′(3) = -1, g′(2) = 5, g(2) = 3, and y = ƒ(g(x)). What is y′ at x = 2?

A: Given:

Q: Find the extrema of f(x,y) = -2x² + y taken on the graph of x + y? = 0.

A:

Q: A function y = f(x) is represented parametrically as follows: x = o(t) = t-5t³ - 20t+7 y = y(t) =…

A:

Q: 4 Let f(x) = 6x°va + || f'(x) =

A: