Question
{4 (03 X = 3 Iex1 T ard tan 9 = 2,72944 2 42 4hen find 4hc valuk ot @65(x-4)
{4 (03 X = 3 Iex1 T ard tan 9 = 2,72944 2 42 4hen find 4hc valuk ot @65(x-4)
Answers
$$ \text { Solve the equation } 3 \tan 2 x-4 \tan 3 x=\tan ^{2} 3 x \tan 2 x $$
This problem Number 45 off. What is equal to thank you. Three X sick three x So what? This is, uh, the militant Al Divide by the X equal to 10-Q 33 x 63 x and this, in turn, can be written eyes 10-Q 3 x 63 x So let us integrate and dx off course let us integrate. So this will become Why equal toe Okay, so let us right is as 10 Squire three x it do 10 3 x in two 63 x dx. So this can Britain is one place more, not one Plus we're Pythagorean identities. Take a square theater. My instance Creditor one So this will be six square three x minus one 10 3 x 63 x dx Now if you substitute 63 x equal to you, we will be getting 363 x 10 3 x d x equal to do you, which means safe three x 10 3 x d x equal to one by three D. So this is just equal to D one by three d this quantity. So, uh, we'll be having you square minus when? Because they you say physical to you. So this is US square minus swim and one by three Deal one by three. Do you? So this will be won by three u que by three minus you policy. So you cube for nine minus. You were three policy. So we have Weichel toe sick three x Q by nine minus 63 x by three plus c. Okay, so this will be there. Answer. Thank you so much.
Okay. This question wants us to find the first and second derivatives of this function. So to start with H prime, we take the derivative of the outside, which is he can't squared, leaving the inside alone. Then we multiply by the derivative of the inside, which is three. So H prime A T is just three times see? Can't squared of three t. Then we have to take another derivative. So for H double prime well, we can see that a c can't squared is just the same thing as putting the whole see can't inside the square. Oh, and this should be with respect to t not X. So now we can use the chain role again to get three times and then we bring the power down in front, keeping the inside alone, decreasing it by one. And then we need the derivative of C can of three t which would be seek and tangent times the derivative of the inside. So three so simplifying our second inter evidence would be three times two times three so 18 and then we have a seek and three t multiplied by a Sikh and three t so that becomes a C can't squared of three t and then we also have a tangent of three T and that's H double crime.
In this problem, we are given that done in worse off X square minus three X plus three equals two by marshall taking turns both sides. This becomes turn off down in rows X squared minus three eggs, last three equals two. Donald by a bashful. We know town of fire before is one and ton of time and worse of excess X itself. So this is extra square -3 x last three Equals to one, or X squared minus three X Plus two equals to one. This is nothing but X -1 -1 into X -2 equals to zero, which means that X is either one or two, that's all.
In this problem, the given equation can be rewritten as And in rows of three x. Plus Cotton balls of three x two gotten worse off three eggs. This is environmental and we used the fact that and then we'll suffix less cotton balls of X. S. Five by two, which makes this as bye bye to moving the terms around. We get to cotton worlds of three x. s. by by 2 -5 x four, which is bye bye for itself or cotton worth of three X. S. Five by eight. Taking court both sides. We have three x. equals to cut off by by eight. This is nothing but Root of two Plus 1. Or we get access Route two Plus 1 divided by three. That's all.