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21. Determine the behaviour of f(x)=\frac{x^{3}-8x-3}{x-3} when x is near 3.
22. The graph of any rational function in which the degree of the numerator is exactly one more than the degree of the denominator will have an oblique (or slant) asymptote.
a) Use long division to show that
y=f(x)=\frac{x^{2}-x+6}{x-2} x
b) Show that this means that the line y = x + 1 is a slant asymptote for the graph and sketch the graph of f.
23. Find the domain of the given function.
a) f(x)=\frac{1}{6^{x}}b)g(x)=\sqrt{3^{x}+1}
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c)h(x)=\sqrt{2^{x}-1}
24. Sketch the graph of the given function. Identify the domain, range, intercepts, and
asymptotes.
b)v=9-3^{\prime}
c.8^{x}=\sqrt{2}
25. Solve the given exponential equation.
26. Let f(x) = 2x, show that f(x+3)=8f(x).
27. Let g(x) = 5*, show that g(x-2) = g(x).
28. Let f(x) = 3, show that \frac{f(x+2)-f(2)}{2}=4f(x)
29. If g(x) = log(x²- 4x+3) , then decide the domain of g and evaluate g(0),g(-1), g(2) and g(4).
30. Sketch the graph of the given function and identify the domain, range, intercepts and asymptotes.
a. f(x) = log(x-3)
b. f(x)=-log_{3}(-x)
c.f(x)=-3+log_{2}\lambda
d. f(x) = 3logs X
31. Sketch the graph of
a. f(x) sec x
c.f(x)=csc~x
e. f(x) = cotx
d. f(x) = sin(x+)
f.f(x)=tan~2x
b. f(x)=1+cos~x
32. Verify the following identities:
a) (sinxcosx)(cscx + secx)=tanxcotx
b) sec²x-csc²xtan²x-cot x
33. Given that tan x , and sin x <0, find sin x, cscx, cos x, secx and cotx.
34. Sketch the graphs of
a. f(x) = sinh x
c. f(x) = cosh x
c. f(x) = tanh x
b. f(x) = csch x
d. f(x) = sech x
f. f(x) = coth x
35. Express
a. 2sinh x + 3 cosh x in terms of e and e
b. 2sinh 4x7 cosh 4x in terms of ex and ex
2e^{x}-e^{-1} in terms of sinh x and cosh x.
d. in terms of sinh x and cosh x and then in terms of coth x.
-3x-3x^{3} in terms of sinh 3x and cosh 3x.
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+1+\frac{8}{x-2}
f)f^{\prime}(x)=\frac{1}{2^{3x}-2}
a)v=5^{-\pi}
i)v=1-e^{-1}
d)v=e^{x-2}
a~e^{3(x^{2}-1)}-1=0
b.100^{x^{2}}-10^{7x-3}=
d.16^{3x-2}=\frac{1}{4}
