1. find the linear approximation to /(x) at x = Xg. Use the linear approximation to estimate the given number. a) f(x) = (x+ 1)i, x=0, VZ4

Q: Find f. f"'(t)  = t   - √t

A: To find f"(t) we integrate f"'(t)

Q: Use the linear approximation of f(x) = /2x - 3 about c = 2 to estimate the value of V1.32 Enter your…

A: Given that: f(x)=2x-3

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: Differentiate the function. r(t) = (3²- + 8)i + r'(t) = (6t)i + ( 132 r'(t) = i + (6t)j r'(t) =…

A:

Q: Use the linearization of the function ƒ(x) = x²/³ at x = 8 to approximate 7.72/3 Enter your…

A:

Q: Let f(x) = x2. Give an equation of the line that intersects the graph of f(x) at x = 0 and x = V2.

A: Given data:     The given function is: f(x)=x2. The first value of x is: x1=0. The second value of x…

Q: Find a linear approximation of the function f(x) = V1-x at a = 0. %3D

A:

Q: 2. Consider the function f(x)=x' –15x² – 37x+51. A Find f(1) В. Rewrite f(x) as a product of linear…

A:

Q: determine the most general function M(x, y) or N(x, y) so that equation is exact.

A: We have to find M(x, y) Or N(x, y).

Q: Solve the following initial value problem (IVP) of y" – 3y – 10y = 2 where y(0) = 2 and y' (0) = -1.…

A:

Q: An object moves in a straight line so that its velocity after t seconds is v(t) = 2/t – t. Determine…

A: Given, Velocity of the particle v(t) = 2t -t Particle is moving in the straight line We have to find…

Q: compute ref(i) when f(z)=sqrt(z-1) and f(0)=-i

A: Given:It is given that  and .To Find:We have to compute .

Q: Let x + y = 28. Find y"(x) at the point (3, 1). "(3) =

A: The solution of the problem is given in the next steps.