The graph of f(x) is shown (see figure). 5x x² + 7 f(x) (a) Find the following limits. L = lim_ f(x) = x → ∞0 K = lim f(x): X→ ∞o x2 = = (b) Determine x₁ and x₂ in terms of ε. X1 M = A = N = Not drawn to scale (c) Determine M, where M > 0, such that [f(x) − L| < ɛ for x > M. (d) Determine N, where N < 0, such that [f(x) − K| < ɛ for x < N.

Q: x-9 Q.4 Let f (x)={ x+3 ,x#3 Find the value of k for which limf(x)=f(3). k,x 3

A: Given

Q: * +(x) = 3x6-4 (x-k)² +17, the value of the parameter k for f(x) to be a function pair IS?

A: For f(x) to be a function pair  it needs to be one-to-one, which means that each input value must…

Q: 1. lim (x – 4)(x² + 8) x→5 2(t-10)² 2. lim t→10 t

A: Let P(x) = a0+a1x+a2x2+.....+anxn be a polynomial, where a0, a1, ...., an are real numbers and n is…

Q: 3. Sketch the graph of a function y(x) with domain (-x, 0) that appears to satisfy each of the…

A: Given: The domain of the function is all real number,  limx→∞y(x)=5limx→-3y(x)=-∞limx→4y(x) does not…

Q: f(x) : II. Determine the limit of the function, g(x) = x² + 2, given its table of values. -3 11 -2…

A: Given :                              g(x) = x2 + 2         (1).…

Q: - 6x - 15 if x -3 Calculate the following limits. Enter "DNE" if the lim f(x) = I -3

A:

Q: Find the limit as x approaches 1 for the function f(x) = 10x + 11. lim (10x+11) = U X-1 (Simplify…

A:

Q: Q1. Find the domain of the functions f(r) = V(2 -1)(r -7) and g(r) = In(r² – 4)(3-r). Also determine…

A: Solution:-   fx=2-x x-7                           &amp; gx=ln x2-4  3-x      Find determine the…

Q: 2. The graph of the function y = f(x) is given below. Using the graph t answer each question. (a)…

A:

Q: 26. ƒ(x) = 2x² − 3x + 1, g(x) = 3√x + 6 - (a) lim f(x) (b) x-4 lim g(x) (c) lim g(f(x)) x→21 x→4

A: f(x) = 2x2 - 3x + 1g(x) =   limx→4 f(x) = limx→4 {2x2 - 3x + 1}                     = 2×42 - 3×4 + 1…

Q: limx→o (t+1)f(t)dt Assume f (0) = 4 %3D 3x2

A: Explanation of the answer is as follows

Q: There are four questions about this problem in the test shown in random order. Out of 1000 customers…

A:

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: Find the limits. F(x) = 2x? - 3x + 4, g(x) = Vx+ 2 (a) lim f(x) x-2 (b) 9(x) lim g(f(x)) = X-2

A: We have to find the limit

Q: Find the limits.

A: The limit of the function is the value at which the arguement tends to a particular value. This…

Q: Select the graph of a function with the given properties. lim f(x) = 2, lim x→ ∞ x→6 lim f(x) = 2, f…

A: Given properties of function

Q: 2 ež h(x) 1 - 4 What is lim h(x)? x→+∞

A:

Q: 2. For h(t)= Vt +12t – 2r² evaluate each of the following limits. (a) lim h(t) (b) limh(t) 『→の

A: We will find out the required limit.

Q: Expand the function p (z + h) as follows. p (z + h) = V(w+h)²–1 Substitute the function p (z + h) in…

A: They are solving derivative for v=1w2-1

Q: Graph the function f(x) = xe2. Find: a. r and y intercepts b. lim re2r x 00 c. Use values (like x =…

A: When f'&lt;0 then function decreasing When f'&gt;0 then function increasing

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: k lim (1+†) k→∞ k

A: We have to find limit

Q: The equation for the line tangent to f (x) at the point (7, 11) is given by y = 12x – 9. Use f(7+h)…

A: The equation of the line tangent is given by y=12x-9 Let ''m'' be the slope of tangent.…