Find lim f(x) if f(x) x->5 = { -x² -1, x #5 -3, x=5

Mathematics

1 answer:

Alex73 [517]2 years ago

3 0

Given

$f(x) = \begin{cases} -x^2 - 1 & \text{if }x \neq 5 \\ -3 & \text{if }x=5 \end{cases}$

we have

$\displaystyle \lim_{x\to5} f(x) = \lim_{x\to5} (-x^2-1) = -5^2-1 = \boxed{-26}$

since we are approaching $x=5$ , so effectively $x\neq 5$ and we use the definition of $f(x)$ under that condition.

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What could be the ordered pairs representing vertices C and D of quadrilateral abcd so that the new fire department is congruent

ohaa [14]

Given that a city grid of Anytown, USA is shown on the grid below. The fire department is represented by quadrilateral RSTU. Another fire department is opening in a different part of the city to maximize fire protection. The size of the new department's property must be congruent to the older department. Vertices A and B are plotted on the grid to represent two vertices of the new fire department quadrilateral ABCD.

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For quadrilateral RSTU to be congruent to quadrilateral ABCD, then RS = AB, RU = AD, ST = BC and TU = CD

Also, the figure ABCD is a result of a rigid body translation of the figure RSTU.

Given that R is at point (-4, 7) and A is at point (4, -1), also given that S is at point (-1, 7) and B is at point (1, -1).

It can be seen that points AB is a result of refrecting points RS across the y-axis and then shifting the resulting points down by 8 units.

Thus, given point T as (-1, 3) and point U as (-4, 3), refrection of points T and U across the y-axis will result in points (1, 3) and (4, 3), then shifting the resulting points down by 8 units will result to points (1, -5) and (4, -5)

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Given the recursive formula for an arithmetic sequence find the common difference and the 52nd term

Mice21 [21]

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