# Calculus questions

### Calculus questions

Section 1 Indices and Logarithms
1) Solve Ln(e6x−4+7)=7 for x.
The answer (correct to 3 decimal places) is x =

Section 2 Functions
2) Let f(x) = −4x+72x−2, find f-1(x).
Answer: (Correct to 3 decimal places) f-1(x) = (-2 x + ) / (x + ).

Section 3 Roots of Equations
3) Solve 3x30x2−124x−96=0.
The roots in ascending order (correct to 3 decimal places) are , and .

Section 4 Inequalities
4) Solve x3 -9 x2 +26 x -24< 0.
Answer: (Correct to 3 decimal places). If there is no upper bound, enter 999 as the value, i.e. x < 999. If there is no lower bound, enter -999 as the value, i.e. -999 < x or x > -999. List your inequalities from the lowest range to the highest range.
x < , < x < , x > ,

Section 5 Simultaneous Equations
5) Solve {3x+4y=4−8x+y=−8
Correct your answers to 3 decimal places. x = , y = .

Section 6 Coordinate Geometry
6) Given point A = (4, 9) and point B = (9, 14). A point C divides the line joining AB in the ratio of 3:8, i.e point C is nearer to point A. What is the equation of the line perpendicular to line AB and passes through point C, in the form of y = mx + c?
Answer: (Correct to 3 decimal places) The equation of the line is y = x +

Section 7 Differentiation 1
7) Given y = Ln(5x+8)+ex25+9x+3−−−−−√. Find dy/dx. Find the gradient of the tangent that touches the graph at x = 2.
Answer: (Correct to 3 decimal places) The gradient of the tangent is m =

Section 8 Differentiation 2 Given y = (2x−7)3e3x−8. When x = 4, dx/dt = 4. What is the dy/dt?
Answer: (Correct to 3 decimal places). dy/dt =

Section 9 Differentiation Optimization
9) Let y = 2 x3 -30 x2 +54 x. Find the maximum point.
Answer: (Correct to 3 decimal places) the maximum point is ( , ).

Section 10 Differentiation Estimation
10) Given y = 2 x3 +7 x2 -2 x -1. Find y when x = 1. Suppose x increases by 0.3, find the first order estimate for y, and second order estimate for y.
Answer: Correct to 3 decimal places.
First order estimate for y = .
Second order estimate for y = .

Section 11 Integration
11) Find ∫10(5x2+8+e9x−3+1−5x+6)dx.

Section 12 Sequences and Series
12) An Arithmetic Progression has the following terms: 2900, 3400, ... . Which term in this sequence would first exceed or equal 75,000? What is the sum from the 1st term to this term?
Answer: It would exceed or equal at the
th term.
(Correct to 3 decial places) The sum from the 1st term to this term =

Section 13 Probability 1
13) Given P(A) = 0.6, P(B) = 0.5, P(A ∪ B) = 0.72. Find P(A | B) and P(B | A).
Answer: (correct to 3 decimal places) P(A | B) =
and P(B | A) =

Section 14 Probability 2
14) A salesman has a success rate of 0.35, i.e. the probability that a passerby will buy the product after his salespitch is 0.35. What is the probability that there are 3 or more passersby out of 4 buying the product after his salespitch? Assume the 4 passersby's decisions are independent of each other.
Answer: P(3 or more passersby out of 4 buying the product after his salespitch) =

Section 15 Statistics
15) Given the following corresponding set of data values for x and y:
x 37 60 80 82
y 38 42 62 90

The population covariance (to 1 decimal place) =
The correlation (to 3 decimal places) =
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### Re: Calculus questions

I understand the fifth task as follows:

$$\begin{array}{|l}3 x +4 y = -8 \\ 4-8x + y = -8 /.(-4) \end{array}$$ $$\Leftrightarrow$$

$$\begin{array}{|l} 3x + 4y = -8 \\ 32x - 4y = 48 \end{array}$$ [We collect them.]

35х=40 $$\Leftrightarrow$$ х=$$\frac{8}{7}$$ [This is substituted in the top (first) equation.]

$$\frac{3.8}{7}$$+4у=-8 $$\Leftrightarrow$$ 4у=-$$\frac{80}{7}$$ $$\Leftrightarrow$$у= -$$\frac{20}{7}$$

Answer: ($$\frac{8}{7}$$;-$$\frac{20}{7}$$)
You can turn ordinary fractions into decimal. Guest

### Re: Calculus questions

I have found your list of questions posted at four different sites. You have the same user name at three of these sites. The visual information posted indicates these questions come from a final assessment"? Are you cheating?
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### Re: Calculus questions

I am an ordinary person (from Europe) who is in love with mathematics .
What fraud (scams) do you see in this Do you see an error in the solution ?
Guest

### Re: Calculus questions

For the fourth task i det an answer: Х$$\in$$[-999;2)$$\cup$$(3;4)
Shall i send the decision ?
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