True/False: If the domain of f(x) is all real numbers and f'(x) <0 for all x, then lim as x goes to infinity of f(x) = - infinity

Q: b) Euler's theorem states that f(:) = "lax, X1 +°"/ax,X2 for functions that are homogenous of degree…

A: Homogeneous Function: A function f of two variables x and y is said to be homogeneous of degree n if…

Q: (-3 if z 2

A: Here is a step by step solution of the problem. We have proved discontinuity at x=2 by evaluation…

Q: If  f′(x) < 0 for 1 <x< 6, then f is decrescent over(1,6) True or false and why

A: If  f′(x) &lt; 0 for 1 &lt;x&lt; 6, then f is decrescent over (1,6) True or false and why

Q: Suppose that f(x)=(x+2)(x-2)^2. (G) Use interval notation to indicate where f(x) is concave down.…

A:

Q: b) Euler's theorem states that f(:) = "/ax, · ×1 +°' /ax, ' x2 for functions that are homogenous of…

A: The given function is: f(x1,x2)=x12+x22 Now, to verify: f=∂f∂x1x1+∂f∂x2x2

Q: 2. The zeros of a function f(x) are 3 and 4, while the zeros of a second function g(x) are 3 and 7.…

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Q: I'm confused on how to put a piecewise function into interval notation

A: To rewrite the definition of the given function using interval notation

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.