The limit of the given function if 
is 64
<h3>Limit of a function</h3>
Given the following limit of a function expressed as;
We are to determine the value of the function
![\frac{1}{4} \lim_{x \to 0} [f(x)]^4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Bf%28x%29%5D%5E4)
This can also be expressed as
![\frac{1}{4} \lim_{x \to 0} [f(x)]^4\\ = \frac{1}{4}(4)^4 \\=1/4\times 256\\=64](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Bf%28x%29%5D%5E4%5C%5C%20%3D%20%5Cfrac%7B1%7D%7B4%7D%284%29%5E4%20%5C%5C%3D1%2F4%5Ctimes%20256%5C%5C%3D64)
Hence the limit of the given function if is 64
Learn more on limit of a function here: brainly.com/question/23935467
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Answer:
The measure of all the angles are;
45°, 135°, 45°, and 135°
Step-by-step explanation:
The given parameters are;
The ratio of two adjacent angles of the parallelogram = 1:3
Let x represent one of the adjacent angles, and let y represent the other adjacent angle
Given that two adjacent angles of a parallelogram are supplementary, we have;
x + y = 180°
x:y = 1:3
Therefore, y = 3 × x = 3·x, which gives;
x + 3·x = 180°
4·x = 180°
x = 180°/4 = 45°
y = 3 × x = 3 × 45° = 135°
Given that opposite interior angles of a parallelogram are equal, we have, the measure of all the angles are;
45°, 135°, 45°, and 135°.
Answer:
See picture:)
Hope that makes sense! If you'd like any more help with maths, I'd be happy to offer online tuition. You can find me at: www.birchwoodtutors.com
Recall that for all t,
cos²(t) + sin²(t) = 1
Now,
x = 5 cos(t) - 7 ⇒ (x + 7)/5 = cos(t)
y = 5 sin(t) + 9 ⇒ (y - 9)/5 = sin(t)
so that substituting into the identity above, we get
((x + 7)/5)² + ((y - 9)/5)² = 1
which we can rewrite as
(x + 7)²/25 + (y - 9)²/25 = 1
(x + 7)² + (y - 9)² = 25
and this is the equation of a circle centered at (-7, 9) with radius 5.
