Question
Evaluate lim tan n+ 0 A graph of some of the first terms of the sequence follows5.54.43.32.21.9 12 15 18 21 24 27 30 33 36 39 42 45 48-l-2.23.3limit =Points possible:License
Evaluate lim tan n+ 0 A graph of some of the first terms of the sequence follows 5.5 4.4 3.3 2.2 1. 9 12 15 18 21 24 27 30 33 36 39 42 45 48 -l -2.2 3.3 limit = Points possible: License
Answers
Evaluate the limits that exist. $$\lim _{x \rightarrow 0} \frac{2 x}{\tan 3 x}$$
In this problem we have to evaluate the limit As X goes to zero of the tangent of three X divided by two X squared plus five X. Now first let's substitute an X equals zero into the limit. To see what indeterminate form we're dealing with. And we get tangent of three times zero divided by two times zero squared Plus five times 0. And we get that the numerator evaluates to zero and the denominator also evaluates to zero. So are given limit is in the 0x0. Indeterminate form. Now from here we can differentiate the numerator and differentiate the denominator as well using low profiles rule and our limit Becomes the second squared of three x. multiplied by the derivative of the angle which is three Divided by the derivative of the denominator which is six X plus five. Now from here we can directly substitute in X equals zero into the limit. And we get seeking squared of three times zero, multiplied by three divided by six times zero plus five, Which evaluates to three x 5 which is a required limit.
Hello. If you have to find this limit for this given function. Every for the limit in this, this will be three in two X zero and 10. 4 into zero. This is also zero. This is the indeterminate form. Indeterminate form. So we will use and hope to lose their he helped us to so we can add limit extra C. Zero differentiation of the turtles three and defenses in of 10 polyps. That is self square foot health into four differences forever is for So we can ask for second swept what it's Now. We will put the limit. Here's this will be three the wild way. four second square zero. This will be costing three into 4. 3 x four. 70. Is what To the value of this limited three x 4. I bought your mystery. Thank you.
In the solution we have to find the value of limit accidents to zero of three times than three X. Negative four times. Then two eggs negative 10 X upon four times x squared times Xanax. So here we know that Ben Ben X 10 3 X value is three times 10 x negative 10 cube bags upon 1 -3 times Danny square at. So now we put here limit extends to zoo of three times three times 10 x negative 10 Cube bags upon 1 -3 times Danny's squad X negative four times to 10 X apart. Want negative. That is quite a negative. Yeah, upon four times x squared times 10 X. So now we simplify this. So here we get limit extends to see you one of full time access choir three times one up on three positive Add up on three on one night, three times dan is quite now you do night one negative Dennis Squad. So now here we get limit accidents to zero. Now we take common eight and we make like denominators. So here we get eight a bone four times access time, two times Dennis quaid eggs upon one negative Dennis quad X times 1 -3 times. That is quite not really right, denominator and united by many square eggs. And after that puts Limit accidents to zero. So here we get full, which is all.
In this problem, we need to evaluate a limit. Now the limit that has been given in this problem is the limit as X tends to zero of three X times stand X divided by sine X. We can rewrite this as the limit as X tends to zero of three X times sin X divided by cause X. Because it in X is equal to sin X. Because X. And in the denominator we have Syntex. So Synnex and Synnex gets cancelled out over here. And what we are left with is limit as x tends to zero of three X times one by cossacks. And using the product rule for the limits, we can write this as the limit as X tends to zero of three X times the limit as X tends to zero of one by cause X. So this will become three times zero by using the direct substitution property. And the second limit will become one divided by the limit as X tends to zero of cost X. So three times zero is zero, and here we have one divided by cost zero, so that would be zero times one divided by one, and that is just equal to zero. Hence the required limit is equal to zero.