MHB Can you help with these calculus questions?

[sarahlee]

Section 1 Indices and Logarithms
1) Solve Ln(e6x−4+7)=7 for x.
The answer (correct to 3 decimal places) is x =
Marks : 1
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
8) 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.
Answer: (Correct to 3 decimal places) the answer is

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) =

 

[MarkFL]

Hello and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Please post each question in a separate thread, along with what you've tried or your thoughts on the problem, and when you are done, let me know so I can delete this thread.

Thanks!

 

[tkhunny]

Section 1 Indices and Logarithms
1) Solve Ln(e6x−4+7)=7 for x.
The answer (correct to 3 decimal places) is x =
Marks : 1
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
8) 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.
Answer: (Correct to 3 decimal places) the answer is

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) =

Posting multiple problems on multiple websites without showing ANY of your own work really is in bad form. In any case, please show YOUR work - one problem at a time, There are many who are willing to HELP. There are a few who are willing just to give out solutions, but most like to discourage such behavior.

 

[MarkFL]

I should also add, that when you re-post each question in separate threads, please be sure the mathematics is formatted such that it is readable and free from ambiguity.

 

[MarkFL]

I saw where these same questions were posted on another site by the same username, and images were posted indicating this is a "Final Assessment" and so I am closing this thread until I hear from the OP (via private message) regarding permission given to seek outside help with a graded assignment.