(a) Given f(x) = a" where a > 1, ƒ-'(x) = loga(x)(b) In the equation A(t) = Aoekt, if k is positive then as t o0, A(t) →%3D0.(c) It is possible for a polynomial p(x) to have a single complex root.(d) Given the following inequality (x- a)(x - b) > 0, we must have thatx - a >0 or x- b > 0.(e) Given the graph of a function f(x), the function g(x)=f(-x) is obtainedby flipping the graph of f(x) across the x axis.(f) A curve in the x y plane defines a function y of x if it passes thevertical line test.(g) A curve in the x y plane is one-to-one if it passes the vertical linetest.(h) For any polynomial f(x) = anx" +x"-1 +is always all real numbers.+a1x+a0; the domain%3D...(i) The graphs of functions and their inverses are always symmetricabout the y axis.(j) The solution to the inequality r- 1 2 is the interval (3, 0).

Hey, since there are multiple subparts posted, we will answer first 3 questions. If you want any…

(a) Given f(x) = a" where a > 1, f-'(x) = loga(x) %3D %3D (b) In the equation A(t) = Agekt, if k is positive then as t 0o, A(t) → %3D 0. (c) It is possible for a polynomial p(x) to have a single complex root.

(a) Given f(x) = a" where a > 1, f-'(x) = loga(x) %3D %3D (b) In the equation A(t) = Agekt, if k is positive then as t 0o, A(t) → %3D 0. (c) It is possible for a polynomial p(x) to have a single complex root.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

(a) Given f(x) = a" where a > 1, ƒ-'(x) = loga(x)
(b) In the equation A(t) = Aoekt, if k is positive then as t o0, A(t) →
%3D
0.
(c) It is possible for a polynomial p(x) to have a single complex root.
(d) Given the following inequality (x- a)(x - b) > 0, we must have that
x - a >0 or x- b > 0.
(e) Given the graph of a function f(x), the function g(x)=f(-x) is obtained
by flipping the graph of f(x) across the x axis.
(f) A curve in the x y plane defines a function y of x if it passes the
vertical line test.
(g) A curve in the x y plane is one-to-one if it passes the vertical line
test.
(h) For any polynomial f(x) = anx" +x"-1 +
is always all real numbers.
+a1x+a0; the domain
%3D
...
(i) The graphs of functions and their inverses are always symmetric
about the y axis.
(j) The solution to the inequality r- 1 2 is the interval (3, 0).

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