EXERCISE 1. The equation below represents the infected class I(t) with t be- ing the time measured in days. A is the infection rate and a is the treatment rate. I' = XI(1000 – I) – al. Answer the following: (a) What is the limit of I(t) if A = 0.005 and a = 7? (b) What is the limit of I(t) id A = 0.005 and a = 2? (c) If A = 0.005, a = 2 and, initially, there are 10 people infected, how many infected people there are after 3 days, i.e. I(3)?

Q: Given f''(x) = 3x – 6 and f'(– 3) = 2 and f( – 3) = - 1. – 1. Find f'(x) = and find f(2) =

A: The objective is to find f'(x) and f(2).

Q: If ƒ(x) ƒ'(x) = - 53 x - 7' what's f'(x)?

A:

Q: Let f(1) = 1, g(1) = -3,h(1) = 2, f'(1) = -1,g'(1) = 2, and h'(1 d f(x) g(x) dx h(x) Find when x =…

A: Please refer to the image below

Q: II. Obtain the required order or level of derivative. 1. y = 3x5 + 4x³ – 4x + 1, find y" 2. f(x)…

A: Solve differentiate

Q: For the function y = h(x) whose graph is shown, find the values of x such that the derivative is…

A: For the given function: y=hx The graph shown is:

Q: Suppose h = fog. Find h'(0) given that f(0) = 8, f'(2) = -7, g(0) = 2, and g'(0) = 3. h'(0) =

A: Given that, ,  and .The aim is to find the value of .

Q: f'(z) = lim Δz-10 f(z + Δz) – f(z) Δz

A:

Q: Your used Chevy’s gas mileage (in miles per gallon) is given as a function M(s) of speed s in miles…

A:

Q: Which derivative rule(s) was (were) usec f(x) = 2 e* + 7lnx - Vx3 1 7 f'(x) = 2 ex + 3. 4 4

A:

Q: Consider the function f in Example 2 in this section. What is f' (1)? f'(1) = -2 What is the average…

A:

Q: Find the derivative of h(x) = O O a.) h'(x)= b.) c.) d.) ܝܕܝ h'(x) = h'(x) = h'(x)= 2 Waiting for…

A: Solve for the derivative

Q: 2. Determine the exact value of f'(2) for f(x) = (2e³ + 3e-6x)5.4,

A:

Q: Given that: f(-3) = 2, f'(-3) = 4, g(-3) = 9, g'(-3) = 7, calculate the following: (fg)'(-3) =…

A:

Q: Let f(x) = 1- 5x2. Use the limit definition of the derivative to show tl f'(x) = –10x

A:

Q: If P(A or B) = 0.801, P(B') = 0.33 and P(A and B) = 0.20. Find i) P(B) ii) P(A)

A: Answer: Given that, P(A or B) = 0.801 P(B') = 0.33 P(A and B) = 0.20

Q: Let f(x) = t° dt. Evaluate the following. f'(x) = f'(5)

A:

Q: 6. FinD F(S) if f(t)= t· cost

A:

Q: 1. It is the process of finding the set of all functions whose derivative is known. B.…

A:

Q: b. A poll commissioned by a politician estimates that t days after he makes a statement denigrating…

A: Given that, St=75t2-3t+25t2+3t+25 (1) Differentiating St, with respect to t.…

Q: Consider the function -3 f(x)=√1+z² (a) Find the linearization of the function f near z = 0. In…

A: Consider the function near (a) The linearization of a function is given by In our case, Evaluating…

Q: The graphs of the function F (left, in blue) and G (right, in red) are below. Let P(x) = F(x)G(x)…

A: Graph of the functions Fx and Gx are given and Px=FxGx and Qx=FxGx. We have to find the values of…

Q: Let f and g be functions such that f(8) = 24. f'(8) = 5. ƒ(24) = 16. f'(24) = −6. g(24)= -29. g'(24)…

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.