Answer with Step-by-step explanation:
We are given that 
We have to prove that why the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form and prove that the limit equals to 0.
Because 
and
We know that cos 0=1 and sin 0=0
Substitute the values then we get
We know that 
is indeterminate form
Hence, the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form.
L'hospital rule:Apply this rule and differentiate numerator and denominator separately when after applying 
we get indeterminate form
Now,using L' hospital rule
because 
Now, we get
Hence,
The first step is 10 - 7 + (2)(14)/4 which equals (2-step) = 3 + 28/4 (3-step) = 3 + 7 (finale-step) = 10
Answer:
15,2% of American men are between 68.6 and 69.4 inches tall.
Step-by-step explanation:
p(69)=0.19 tells you that 19% of all American men are 69in tall. Now, we want to know what percentage of those men are exactly between 68.6 and 69.4 inches tall. We only need to multiply the given density function by the gap between the two heights we are looking for, so:
0.19 * (69.4-68.6) = 0.19*0.8 = 0.152*100 = 15,2%
To calculate the value of the half life we proceed as follows;
a/2=ae^(-2.360t)
the a(s) will cancel and we shall remain with:
1/2=e^-2.360t
introducing the natural logs we get:
ln (1/2)=ln e^(-2.360t)
ln(1/2)=-2.360t
hence;
t=(ln 0.5)/(-2.360)
t=0.294
the answer is t=0.294
