When x<span> approaches to </span><span>+∞</span><span> the function </span><span>e^<span>3x</span></span><span> becomes much bigger then </span><span>e^<span>−3x</span></span><span>, which obviously means that </span><span>e^<span>−3x</span></span><span> can be neglected in both numerator and denominator.
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Here's how I figured this out:
</span><span>lim <span>x →+∞ </span></span>= (<span><span><span>e^(<span>3x))</span></span>− (<span>e^(<span>−3x)) / (</span></span></span><span><span>e^<span>3x)) </span></span>+ (<span>e^(<span>−3x)) </span></span></span></span>= <span>lim <span>x → +∞ </span></span><span><span>e^<span>3x / </span></span><span>e^<span>3x </span></span></span>= 1
14 times 1 is 14
14 times 2 is 28
14 times 3 is 42
Answer:
Perimeter = 18.7 units
Area = 13.5 units²
Step-by-step explanation:
Perimeter of ADEC = AD + DE + EC + AC
Length of AD = 3 units
By applying Pythagoras theorem in ΔDBE,
DE² = DB² + BE²
DE² = 3² + 3²
DE = √18
DE = 4.24 units
Length of EC = 3 units
By applying Pythagoras theorem in ΔABC,
AC² = AB² + BC²
AC² = 6² + 6²
AC = √72
AC = 8.49 units
Perimeter of ADEC = 3 + 4.24 + 3 + 8.49
= 18.73 units
≈ 18.7 units
Area of ADEC = Area of ΔABC - Area of ΔBDE
Area of ΔABC = 
= 
= 18 units²
Area of ΔBDE = 
= 
= 4.5 units²
Area of ADEC = 18 - 4.5
= 13.5 units²
Answer:
Area = πx² + x² or x²(π + 1)
Step-by-step explanation:
The area of the heart = area of a circle + area of the square
Note:
1. The 2 semicircles makes 1 full circle
2. The diameter of the circle = the side length of the square
Thus:
Area of the heart = πr² + s²
Where,
r = x
s = x
Formula for area of the heart = π(x²) + x² = πx² + x²
Area = x²(π + 1)
