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Kamila [148]
3 years ago
12

Show why the limit as x approaches 0 (csc(x)-cot(x)) involves an indeterminate form, and then prove that the limit equals 0.

Mathematics
1 answer:
Nadusha1986 [10]3 years ago
5 0

Answer with Step-by-step explanation:

We are given that \lim_{x\rightarrow 0 }(csc(x)-cot(x))

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.

\lim_{x\rightarrow 0 }(\frac{1}{sinx}-\frac{cosx}{sinx})

Because csc(x)=\frac{1}{sinx} andcot(x)=\frac{cosx}{sinx}

\lim_{x\rightarrow 0 }(\frac{1-cosx}{sinx})

\frac{1-cos0}{sin0}

We know that cos 0=1 and sin 0=0

Substitute the values then we get

\frac{1-1}{0}=\frac{0}{0}

We know that \frac{0}{0} 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 \lim_{x\rightarrow a }we get indeterminate form\frac{0}{0}

Now,using L' hospital rule

\lim_{x\rightarrow 0 }\frac{0+sinx}{cosx}

because \frac{dsinx}{dx}=cosx,\frac{dcosx}{dx}=-sinx}

Now, we get

\lim_{x\rightarrow 0 }\frac{sinx}{cos x}

\frac{sin0}{cos0}

\frac{0}{1}=0

Hence,\lim_{x\rightarrow 0 }(csc(x)-cot(x))=0

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Simplify <br> 3 2/3 - 2 3/4 =
Rasek [7]

Answer: 11/12

Step-by-step explanation:

1. To solve this problem you can transform the mixed numbers given in the problem to fractions, as you can see below:

3 2/3=(3*3+2)/3=11/3

2 3/4=(4*2+3)/4=11/4

2. Now you must make the substraction of the fraction:

11/3-11/4=11/12

3. Therefore, the answer is 11/12

6 0
3 years ago
Please help will mark as brainiest
Damm [24]
The answer is 41% hope this helps
6 0
3 years ago
HELP!!! Use the factor Theorem to determine whether the binomial x+1 is a factor of the polynomial function f(x) =2x^3-9x^2+13x-
Dovator [93]

ANSWER

A. No because f(c)=-30

EXPLANATION

The given polynomial is

f(x) =2x^3-9x^2+13x-6

If x+1 is a factor , then f(-1) must evaluate to zero.

f( - 1) =2( - 1)^3-9( - 1)^2+13( - 1)-6

f( - 1) =2( - 1)-9( 1)+13( - 1)-6

f( - 1) = - 2-9 - 13-6

f( - 1) = -11 - 19

f( - 1) = - 30

Since f(-1) is not equal to zero, x+1 is not a factor of

f(x) =2x^3-9x^2+13x-6

6 0
3 years ago
What is the standard deviation of the following data set rounded to the nearest tenth? 56 ,78 ,123 , 34, 67, 91, 20
quester [9]

Answer:

The standard deviation of the following data set is 32.2

Step-by-step explanation:

step 1

Find the mean

we have

[56,78,123,34,67,9,20]

Sum the data and divided by the number of elements

[56+78+123+34+67+91+20]/7=469/7=67

step 2

For each number: subtract the Mean and square the result

[(56-67)^{2},(78-67)^{2},(123-67)^{2},(34-67)^{2},(67-67)^{2},(91-67)^{2},(20-67)^{2}]

[121,121,3,136,1,089,0,576,2,209]

step 3

Work out the mean of those squared differences

[121+121+3,136+1,089+0+576+2,209]/7=1,036

This value is called the "Variance"    

step 4

Take the square root of the variance

standard\ deviation=\sqrt{1,036}=32.2

6 0
3 years ago
I NEED HELPPPP PLEASE RN!!
Romashka-Z-Leto [24]

Answer:

is A

Step-by-step explanation

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3 0
3 years ago
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