Use the graph to estimate the specified limit. 1) Find lim x(-1)- f(x) and lim x(-1)+ f(x) 1) A) -7; -5 B) -5; -2 C) -2; -7 D) -7; -2 2) Find lim x??/2)- f(x) and lim x??/2)+ f(x) 2) A) 2; 6 B) ?;...

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Use the graph to estimate the specified limit. 1) Find lim x(-1)- f(x) and lim x(-1)+ f(x) 1) A) -7; -5 B) -5; -2 C) -2; -7 D) -7; -2 2) Find lim x??/2)- f(x) and lim x??/2)+ f(x) 2) A) 2; 6 B) ?; ? C) ? 2 ; ? 2 D) 6; 2 1 Determine the limit by sketching an appropriate graph. 3) lim x  6+ f(x), where f(x) = -5x + 3 for x < 6 3x + 4 for x L 6 3) A) -27 B) 4 C) 22 D) 5 Find the limit. 4) lim h0+ h2 + 5h XXXXXXXXXXh 4) A) Does not exist B XXXXXXXXXXC) 5 10 D) 1 2 Find the limit using lim x=0 sinx x = 1. 5) lim x0 x sin 3x 5) A) 3 B) does not exist C) 1 D XXXXXXXXXXlim x0 sin 4x sin 5x 6) A) does not exist B) 0 C) 5 4 D XXXXXXXXXXlim x0 sin x cos 4x x + x cos 5x 7) A) 1 2 B) 4 5 C) does not exist D) 0 2 Find all points where the function is discontinuous XXXXXXXXXXA) None B) x = 2 C) x = 4 D) x = 4, x = XXXXXXXXXXA) None B) x = 0 C) x = -2, x = 0, x = 2 D) x = -2, x = 2 Determine the limit by sketching an appropriate graph. 10) lim x  7- f(x), where f(x) = -3x - 4 for x < 7 5x - 3 for x L 7 10) A) 32 B) -25 C) -3 D XXXXXXXXXXlim x  -4+ f(x), where f(x) = 2x -4 K x < 0, or 0 < x K 3 2 x = 0 0 x < -4 or x > 3 11) A) -8 B) -0 C) Does not exist D) 6 Find numbers a and b, or k, so that f is continuous at every point. 12) f(x) = x2, ax + b, x + 12, x < -4 -4 K x K -3 x > XXXXXXXXXXA) a = -7, b = 12 B) a = 7, b = -12 C) a = -7, b = -12 D) Impossible 13) f(x) = x2, kx, if x K 3 if x > 3 13) A) k = 1 3 B) k = 9 C) k = 3 D) Impossible Find the limit. 14) lim xgQ XXXXXXXXXX/x XXXXXXXXXX/x2) 14) A XXXXXXXXXXB) Q C) 2 3 D) g Q 15) lim xgQ cos 5x x 15) A) 1 B) 0 C) 5 D) g Q Divide numerator and denominator by the highest power of x in the denominator to find the limit. 16) lim xgQ 3 x - 6x - 5 7x + x2/ XXXXXXXXXXA XXXXXXXXXXB) g Q C XXXXXXXXXXD) 0 4 Find the limit. 17) lim x  10- 1 x XXXXXXXXXXA) 0 B) Q C) g Q D XXXXXXXXXXlim x  -3+ x2 - 8x + 15 x3 - 9x 18) A) g Q B) Does not exist C) 0 D) Q 19) lim xQ x2 + 3x - x2 - 5x 19) A) 4 B) - 1 C) 8 D) does not exist Provide an appropriate response. 20) Let lim x  10 f(x) = -3 and lim x  10 g(x) = -9. Find lim x  10 [f(x) + g(x)]2. 20) A) 144 B) 6 C) 90 D XXXXXXXXXXLet lim x  3 f(x) = -9 and lim x  3 g(x) = -4. Find lim x  3 [f(x) · g(x)]. 21) A) 36 B) -4 C) -13 D XXXXXXXXXXLet lim x -4 f(x) = 1024. Find lim x -4 log4 f(x). 22) A) 5 B) -4 C) 5 4 D XXXXXXXXXXLet lim x  6 f(x) = 2. Find lim x  6 (-3)f(x). 23) A) -3 B) 9 C) 729 D) 2 Find the limit. 24) lim x0 (3 sin x XXXXXXXXXXA) 3 B XXXXXXXXXXC) 0 D) -1 Find numbers a and b, or k, so that f is continuous at every point. 25) f(x) = x2, kx, if x K 2 if x > 2 25) A) k = 4 B) k = 1 2 C) k = 2 D) Impossible
Answered Same DayDec 20, 2021

Solution

David answered on Dec 20 2021
3 Votes
1) From the graph, we can see that as x approaches -1 from negative side , y becomes -2 and as it
eaches positive side , y becomes -7 C) -2; -7
2) From the graph, we can see that as x approaches π/2 from negative side , y becomes 6 and as it
eaches π/2 positive side , y becomes 2 D) 6; 2
3)
x y
-5 28
-3 18
-1 8
1 -2
3 -12
5 -22
6 -27
6 22
8 28
10 34 -40
-30
-20
-10
0
10
20
30
40
-10 -5 0 5 10 15


C) 3x+4 = 3*6+4 = 22
4) Using L’Hospital’s rule,

√ √



(Ans is option B)
5)




(Ans is option D)
6)


(


) (
...
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