dh The level of water h in a water clock is governed by the equation -h/3 dt • Sketch the slope field in the upper half-plane h > 0. • Use Separation of Variables to find a solution in the domain (-x, 1] with h(1) = 0. • Prove that the function h(t) : your solution to (b),t < 1, 0, t > 1 is differentiable and satisfies the differential equation. Draw the corresponding solution curve on your picture for (a).

Q: Consider the function f(x)=(x4 -2x3)/(x-2). Verify that Lim (x->2) f(x)=8. In order to guarantee…

A: Consider the function f(x)=(x4 -2x3)/(x-2). To Verify that limx→2f(x) = 8

Q: 3n Find lim,→0 (1+ )'

A: Here,

Q: Consider the piece -wise function h): = (x)4 x²-2x +3 for x 2 Find lim hx) Find is h«) Contiouous?…

A:

Q: 2. Explain what it means to say lim f(x) does not exist. Again, be sure to explain the concepts!!

A: Given :limx→3fx does not exist

Q: Prove that limxc f(x) = Lis equivalent to limxc [ f(x) − L] = 0.

A:

Q: to if iz fx) < x (x)_ +4x+4,for allx, find Lim f(x)

A:

Q: Determine lim X- • ot s/x 7 Sinx

A: limx→0+5x-7sinx

Q: 2- Determine lim[ v( x-1000)+10]/x x-0

A: Given problem:-

Q: lim

A:

Q: 2. Consider f(x)=x² – 4x + 2 a) lim f(x) x-2 b) lim f(x) x-4 c) lim f(x) We X-1

A:

Q: Graph of y = B(t) y = B(1) a) Evaluate lim B(t). t-2+ b) Evaluate 奥B(). →2- c) Evaluate B(2)

A: Topic - value of limit of function From graph Note - as per bartleby Guidelines We are supposed To…

Q: Use l’Hospital's Rule to show that lim 1+ X. = e. コ

A:

Q: Explain why: limx→a−b f(x) = limx→a f(x − b).

A:

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.