In Problems 1–8, express the relationship between f′ ( x ) and f ( x ) in words, and write a differential equation that f ( x ) satisfies. For example, the derivative of f ( x ) = e 3 x is 3 times f ( x ); y ′ = 3y. ( If necessary, review Section 3.4 ). 5. f ( x ) = 3.2 e x 2
In Problems 1–8, express the relationship between f′ ( x ) and f ( x ) in words, and write a differential equation that f ( x ) satisfies. For example, the derivative of f ( x ) = e 3 x is 3 times f ( x ); y ′ = 3y. ( If necessary, review Section 3.4 ). 5. f ( x ) = 3.2 e x 2
Solution Summary: The author explains that the relationship between fprime '(x)' and
In Problems 1–8, express the relationship between f′(x) and f(x) in words, and write a differential equation that f(x) satisfies. For example, the derivative of f(x) = e3xis 3 times f(x);y′ = 3y. (If necessary, review Section 3.4).
Find all values of x for the given function where the tangent line is horizontal.
3
=√x³-12x² + 45x+5
Find the equation of the tangent line to the graph of the given function at the given value of x.
6
f(x) = x(x² - 4x+5)*; x=2
7.
Suppose that X is a set, that I is a nonempty set, and that for each i Є I that Yi
is a set. Suppose that I is a nonempty set. Prove the following:2
(a) If Y; CX for all i EI, then Uiel Yi C X.
¹See Table 4.8.1 in zyBooks.
Recall:
Nie X₁ = Vi Є I (x = X₁) and x = Uier X₁ = i Є I (x Є Xi).
(b) If XCY; for all i Є I, then X Ciel Yi.
(c) U(x)=xnUY.
iЄI
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Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY