Question

Is the function defined by x^2 - sin x + 5 continuous at x = pi?

Answer 1

Hint : sum of two continuous functions is continuous

Answer 2

you don't need to do any work if you're allowed to use that fact

Answer 3

otherwise you may use LHL=RHL=f(pi) to prove continuity

Answer 4

Sum of two continuous functions is continuous, how do I go down this method?

Answer 5

x^2+5 is continuous as all polynomials are continuous

-sinx is another familiar continuous function

so the sum of these will be another continuous function

Answer 6

based on your previous problems i don't think you're allowed to finish it off simply like that

Answer 7

Polynomials and trig functions are both continuous? even exponents?

Answer 8

All polynomials are continuous

sinx and cosx are continuous


you need to know them before using "sum of two continuous function... " thingy

Answer 9

so f(x) = sin x + cos x
f(x) = sin x - cos x
f(x) = sinx . cos x

Are all continuous just because they are trig functions?

Answer 10

I never said all trig functions are continuous

Answer 11

sinx and cosx are continuous

so their sum, sinx+cosx is also continuous

Answer 12

hey you don't need all this for exam on 16th

Answer 13

i feel like your prof wants you to use LHL=RHL=f(pi) and finish off

Answer 14

No its a question in my book, f(x) = sin x + cos x

I have about 9 questions with trig functions in the piecewise type

Answer 15

whats the complete question ?

Answer 16

um f(x)=
kx + 1, if x < or = pi
cos x, if x > pi

find k

do you want me to post a new question for this?

Answer 17

you may use LHL=RHL=f(a) for all these problems

may be forget about "sum of two continuous functions if continuous" fact for now

Answer 18

I presume you're given that f(x) is a continuous function ?

Answer 19

```
f(x)= kx + 1, if x < or = pi
cos x, if x > pi
```

Answer 20

Since f(x) is continuous at x=pi, the left and right limits must be equal :
\[ \large \lim\limits_{x\to \pi^{-}} f(x) =\lim\limits_{x\to \pi^{+}} f(x) \]
\[\large k\pi+1 = \cos(\pi)\]

solve \(k\)

Answer 21

okay im a little stuck, can you solve this for me?

Answer 22

Since f(x) is continuous at x=pi, the left and right limits must be equal :
\[ \large \lim\limits_{x\to \pi^{-}} f(x) =\lim\limits_{x\to \pi^{+}} f(x) \]
\[\large k\pi+1 = \cos(\pi)\]
\[\large k\pi+1 = -1\]
\[\large k\pi = -2\]
\[\large k = -\dfrac{2}{\pi}\]

done !!!

Answer 23

Easy..

Answer 24

That's why.. I put cos(pi) as 1..

Answer 25

Got it, brb attempting all 8 questions under this mini-section

Answer 26

looks all of them can be solved using LHL=RHL=f(a) trick
just tag me if you feel stuck.. il be around mostly...