Can someone help me with my homework...? Its about graphing functions and tables, I'll post it right now! But can someone who kn
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Hello Meggieh821, to find the lim as x approaches 0 we can check this by inserting a number that is close to 0 that is coming from the left and from the right.
For instance, we can find the lim by using the number -.00001 for x and solve
<span>csc(3x) / cot(x)
</span>csc(3*-.00001) / cot(-.00001) = .333333... = 1 /3
We also need to check coming from the right. We will use the number .00001 for x
csc(3x) / cot(x)
csc(3*.00001) / cot(.00001) = .333333... = 1 /3
So since we are getting 1/3 from the left and right we can say as x approaches 0 the limit is 1/3
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For instance, we can find the lim by using the number -.00001 for x and solve
<span>csc(3x) / cot(x)
</span>csc(3*-.00001) / cot(-.00001) = .333333... = 1 /3
We also need to check coming from the right. We will use the number .00001 for x
csc(3x) / cot(x)
csc(3*.00001) / cot(.00001) = .333333... = 1 /3
So since we are getting 1/3 from the left and right we can say as x approaches 0 the limit is 1/3
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(tanθ + cotθ)² = sec²θ + csc²θ
<u>Expand left side</u>: tan²θ + 2tanθcotθ + cot²θ
<u>Evaluate middle term</u>: 2tanθcotθ = = 2
⇒ tan²θ + 2+ cot²θ
= tan²θ + 1 + 1 + cot²θ
<u>Apply trig identity:</u> tan²θ + 1 = sec²θ
⇒ sec²θ + 1 + cot²θ
<u>Apply trig identity:</u> 1 + cot²θ = csc²θ
⇒ sec²θ + csc²θ
Left side equals Right side so equation is verified
