Find the constants a so that the function is continuous on the entire...

J

Jason D

New member
...line?(10 POINTS BEST ANSWER, NO JOKE)? Find the constants a so that the function is continuous on the entire line:

f(x) = {

(x^2 - a^2) / (a - x), x is not equal to a
8, x = a

}

[A] a = 8
a = 4
[C] a = -4
[D] none of these


Here is a similar questions but a little bit different

Find the constants a so that the function is continuous on the entire line:

f(x) = {

(x^2 - a^2) / (x - a), a is not equal to a
6, x = a

}

[A] a = 3
a = -3
[C] a = 6
[D] none of these

I think the answer to the first question is B, but I'm not sure at all, so please try to answer BOTH questions

10 POINTS WILL BE AWARDED TO THE BEST ANSWERER
 
1) Where f(x) â‰* a, f(x) = (x - a) * (x + a) / (a - x) = -x - a

Since f(a) is defined as 8, -x - a must = 8. Therefore, as x->a f(x) =8 and a must be -4 so that -x - a = 4 + 4 = 8.

The answer is (A) a = 8 <---------------------- Answer
-----------------------------------

(2) Again, where x â‰* a, (x^2 - a^2) / (x - a) = x + a. Since we want f(x) to be 6 at a, x + a -> a + a = 6 as x->a,

so the answer is (x + a) = 6 and a must therefore a = 3.

The answer to question (2) is (A) a = 3. <---------------------- Answer
.
 
1) Where f(x) â‰* a, f(x) = (x - a) * (x + a) / (a - x) = -x - a

Since f(a) is defined as 8, -x - a must = 8. Therefore, as x->a f(x) =8 and a must be -4 so that -x - a = 4 + 4 = 8.

The answer is (A) a = 8 <---------------------- Answer
-----------------------------------

(2) Again, where x â‰* a, (x^2 - a^2) / (x - a) = x + a. Since we want f(x) to be 6 at a, x + a -> a + a = 6 as x->a,

so the answer is (x + a) = 6 and a must therefore a = 3.

The answer to question (2) is (A) a = 3. <---------------------- Answer
.
 
1) Where f(x) â‰* a, f(x) = (x - a) * (x + a) / (a - x) = -x - a

Since f(a) is defined as 8, -x - a must = 8. Therefore, as x->a f(x) =8 and a must be -4 so that -x - a = 4 + 4 = 8.

The answer is (A) a = 8 <---------------------- Answer
-----------------------------------

(2) Again, where x â‰* a, (x^2 - a^2) / (x - a) = x + a. Since we want f(x) to be 6 at a, x + a -> a + a = 6 as x->a,

so the answer is (x + a) = 6 and a must therefore a = 3.

The answer to question (2) is (A) a = 3. <---------------------- Answer
.
 
1) Where f(x) â‰* a, f(x) = (x - a) * (x + a) / (a - x) = -x - a

Since f(a) is defined as 8, -x - a must = 8. Therefore, as x->a f(x) =8 and a must be -4 so that -x - a = 4 + 4 = 8.

The answer is (A) a = 8 <---------------------- Answer
-----------------------------------

(2) Again, where x â‰* a, (x^2 - a^2) / (x - a) = x + a. Since we want f(x) to be 6 at a, x + a -> a + a = 6 as x->a,

so the answer is (x + a) = 6 and a must therefore a = 3.

The answer to question (2) is (A) a = 3. <---------------------- Answer
.
 
1) Where f(x) â‰* a, f(x) = (x - a) * (x + a) / (a - x) = -x - a

Since f(a) is defined as 8, -x - a must = 8. Therefore, as x->a f(x) =8 and a must be -4 so that -x - a = 4 + 4 = 8.

The answer is (A) a = 8 <---------------------- Answer
-----------------------------------

(2) Again, where x â‰* a, (x^2 - a^2) / (x - a) = x + a. Since we want f(x) to be 6 at a, x + a -> a + a = 6 as x->a,

so the answer is (x + a) = 6 and a must therefore a = 3.

The answer to question (2) is (A) a = 3. <---------------------- Answer
.
 
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