Question: Exercise1.1(no. 4)
4) Forthefunctionfgraphedintheaccompanyingfigure,find
(a) lim
x→2−
f(x) (b) lim
x→2+
f(x) (c) lim
x→2
f(x) (d) f(2).
Exercise1.2(no. 5,9,29)
Findthelimits.
(5) lim
x→3
x2−2x
x+1 (9) lim
x→−1
x2+6x+5
x2−3x−4 (29) lim
x→9
x−9 √x−3
Exercise1.3(no. 14,17,23,25)
Findthelimits.
(14) lim
x→+∞
5x2−4x
2x2+3 (17) lim
x→−∞
x−2
x2++2x+1
(23) lim
x→+∞
3
2+3x−5x2
1+8x2
(25) lim
x→−∞
√5x2−2
x+3
Exercise1.5(no. 15,29a)
15) Findvaluesofx, ifany,atwhichf isnotcontinuous: f(x)= x
2x+2+x
29a) Findavalueoftheconstantk, ifpossible,thatwillmakethefunctioncontinuous
everywhere.
f(x)= 7x−2, x≤1
kx2, x>1
1. **Problem statement:** Find the limits and continuity values as requested in Exercise 1.1 no.4.
2. **(a) Find** $\lim_{x \to 2^-} f(x)$: This is the left-hand limit as $x$ approaches 2.
3. **(b) Find** $\lim_{x \to 2^+} f(x)$: This is the right-hand limit as $x$ approaches 2.
4. **(c) Find** $\lim_{x \to 2} f(x)$: The limit exists if and only if the left and right limits are equal.
5. **(d) Find** $f(2)$: The function value at $x=2$.
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Since the function graph is not provided, we cannot numerically evaluate these limits or $f(2)$. The problem requires the graph to read values.
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**Note:** The user asked multiple problems but per instructions, only the first problem is solved here.
**Final answer:** Cannot determine limits or $f(2)$ without the graph.