A) f(x)=3-7x
Limit f(x) as x tends to 2 is 3-7×2= 3-14 = -11.
|f(x)-L| = | 3-7x-(-11)| =|14-7x| = 7|2-x| = 7|x-2|
let |f(x)-L| < epsilon say e
i.e. 7|x-2| <e this implies |x-2|< e/7 say delta, so for all epsilon >0 , there exists delta >0 such that |f(x)-L| < epsilon , whenever |x-a|< delta, hence proved.
B) Triangular inequality states as |x+y| <= |x|+|y|.
Now let x= a-b and y=b
We get |x+y| = |a-b+b|=|b| and |x|+|y| = |a-b|+|b|
Hence |a| <= |a-b|+|b| which implies |a|-|b|<=|a-b| hence proved .
(A SHOW Lin (3-7x)=-11 USING X - 2 S-€ Definitiow. THE STATE THE TRIANGLE IN EQUALITY,...
f(3) = 7x + 11 is given. a) Prove that f is one-to-one using the definition of a one-to-one function. b) Find the inverse function f-'(x).
please solve 2 to 6 with details
Advanced Calculus: HW 3 (1) Suppose that a E R has the following property: for all n e N, a < Prove that a<0. (2) Prove that the set of integers Z is not dense in R (3) Let A = {xeQ: >0}. Determine whether A is dense in R, and justify your answer with a proof. (4) Find the supremum of the set A= {a e Q: <5} (5) Let a >...
For the function f(x)=x" - 6x + 7x-2, state: a) the maximum number of real zeros that the function can have: b) the maximum number of x-intercepts that the graph of the function can have; and c) the maximum number of turning points that the graph of the function can have. The function f(x)=x" - 6x + 7x-2 has a maximum of real zeros. The function f(x)=x" - 6x®,+ 7x-2 has a maximum of x-intercepts. The function f(x)=x" - 6x...
3. Evaluate the integral S Tz2+9)(x-2) -7x-12dx.
Due Mon 06/01/2020 11:59 pm Show Intro/Instructions If f(x) = 3x2 - 7x + 5, find the following f'(x) = Preview f'(2) = Preview Find the equation of the tangent line to the parabola y = 3x² - 7x +5 at the point (2, 3). The equation of this tangent line is y = mx + b where: m = Preview Preview b= Get help: Video
Use the definition of the fact that f(x) is O(g(x)) to show that: 1. 7x^2 is O(x^2) 2. x^4 + 9x^3 + 4x + 7 is O(x^4) 3. (x^2+1) / (x+1) is O(x) Hint: Try to simplify algebraic expression.
Find the indicated intercept(s) of the graph of the function +8x 2 +7x-3 x-intercepts of f(x) O A. (0,0),(-8,0) O B. (8.0) O C. (0.0). (8.0) O D. (-8.0)
please answer and show all steps
(3) Using the Law of Sines, solve the non-right triangle where B=5°, A= 10°, c=5 (4) Using the Law of Sines, solve the non-right triangle where b=2, c=3, B = 40° I
The function f(x) = 3-7x is one-to-one. 5+11x (a) Find the inverse of f. (b) State the domain and range of f. (c) State the domain and range of f-1.
1) Use Long and Synthetic Division to divide 2x *-7x-6 by * - 2. State the quotient qx). and the remainder (x) a) Long Division b) Synthetic Division Quotient (x) - Remainder r(x) Quotient (x) - Remainder r(x) =