# Pre- Calculus

21,887 results, page 99
1. ## Calculus with analytic geometry

What is the range and domain, x and y intercepts, symmetry and asymptote of this given equation, f(x) = 2x^2 - 8 / x-1
2. ## Calculus

I am having great difficulty with this any help would be appreciated. Write this expression in the form e^kx for a suitable constant k.? (e^4x * e^6x)^3/5, 1/e-2^x
3. ## Calculus - Integrals

The region bounded by y=x^2, x=y^2 is rotated about the line y=-3. The volume of the resulting solid is:
4. ## calculus

solve the following inequality. write your solution in interval notation. x^3+9x^2-108 less than or equal to 0
5. ## calculus

find the area of a rectangle bounded by the axes and one of its corner is a point in a curve y=1/x.
6. ## calculus

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (e^x − e^−x − 2x)/(x − sin(x))
7. ## Calculus Grade 12 University

8. Find the vector equation of the line in which the 2 planes 2x - 5y + 3z = 12 and 3x + 4y - 3z = 6 meet.
8. ## CALCULUS

Find the critical numbers of each given function. (a) f(x)=3rt(x^(2)-x (b) g(x)=2sinx+2cos^(2)x, 0 <=x<=2pie
9. ## Calculus

Find the derivative of the given function w=((t^3)+8)^103 Isnt the answer 309t((t^3)+8)^102
10. ## calculus 2

Sketch the region enclosed by the given curves. Find its area. y=7cos pi x, y=12x^2-3
11. ## calculus

Find the volume of the solid formed by rotating the region enclosed by y=e^(3x)+2, y=0, x=0, and x=.2 about the y-axis

1. What is the maximum integer n such that 3^n is a factor of the product of all the odd inegers between 1 and 200?
13. ## calculus

Find the volume of the solid formed by rotating the region enclosed by y=e^(3x)+2, y=0, x=0, and x=.2 about the y-axis
14. ## calculus

Find the volume of the solid formed by rotating the region enclosed by y=e^(3x)+2, y=0, x=0, and x=.2 about the y-axis
15. ## calculus

Evaluate the following limit: lim x --> negative infinity 9 square root over x^2-1 divided by x + 4
16. ## calculus

Find the length of the entire perimeter of the region inside r = 16sin(theta) but outside r = 4
17. ## Calculus-Derivatives

How is 6#sin(#x-1)/cos^3(#x-1) the derivative of f(x)= 3sec^2(#x-1)? #= Pi (I coulnd't find the symbol...sorry.)
18. ## calculus

Find a point c satisfying the conclusion of the Mean Value Theorem for the following function and interval. f(x)=x^{- {6}}, \qquad[1, 2] c =
19. ## calculus

Integral High value= 4 lower value=0 f(x)dx f(x) = 2, x < 2 x, x ≥ 2 It's asking me to use geometric formulas to solve this without a shape given. What am I supposed to do?
20. ## Calculus help

f is a function that is differentiable for all reals. The value of f ′(x) is given for several values of x in the table below. x –8 –3 0 3 8 f ′(x) 5 4 0 –2 –4 If f ′(x) is always decreasing, which statement about f(x) must be true?
21. ## Calculus

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim (tan(7x))^x x~>0
22. ## Calculus

How do I take the indefinite integral of (5-x)/(2x^2+x-1)? I've tried splitting it into two integrals and even completing the square on the bottom but neither of those led me anywhere. Help?

Evaluate each indefinite integral. Use the substitution method. X square root (x+3) dx
24. ## Calculus

y=sqrt(x)^1/x. Find dy/dx That is to the power of 1/x So to start this do I need to take Ln on both sides and then use a logarithm property? Ln(y)=lnx^1/2x?
25. ## Calculus

Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface r(u,v) =(2u, 3u^2+5v, -4v^2) at the point (0,-10,-16)
26. ## Calculus

Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface r(u,v) =(2u, 3u^2+5v, -4v^2) at the point (0,-10,-16)
27. ## calculus

Find the volume of the solid obtained by rotating the region bounded by y=4x^2,x=1,y=0 about the x-axis.
28. ## calculus

Consider the following function. f(x) = (6 − x)e^−x (c) Find the point of inflection. (If an answer does not exist, enter DNE.) (x,y)=( , )
29. ## Calculus

Find the derivative: h(x)=7x/sqrt(5-2x) Using the chain rule...I figured out my previous post.
30. ## Calculus

I need help with this problem: Let f(x)= sqrt(x-3) and g(x)=(x^2)+1 a. Compute g(f(x)) b. State the domain of g(f(x)) in interval notation. I got x-2 for a, but i do not understand b. Help please
31. ## Calculus AB

If f(x) is differentiable for the closed interval [-3, 2] such that f(-3) = 4 and f(2) = 4, then there exists a value c, -3 < c < 2 such that f(c) = 0 f '(c) = 0 f (c) = 5 f '(c) = 5 Not really sure where to start here. No textbook and my teacher
32. ## Calculus

Use the binomial Theroum to expand the expression and express the results in simplified form (3X + 2)^3
33. ## Calculus

Find the average value of the function defined by f(x)= x^2 sin 3 x^3 on the interval [0, 3rd Root (pi)]
34. ## Calculus - fundamental theorems

d/dx integral e^t^2 dt from 1 to x^3 Please help. I think I'm supposed to use substitution for the x^3 and then apply the chain rule but I'm not sure how to do that.
35. ## Calculus

Represent the function f(x)= 10ln(8-x) as a Maclaurin series and Find the radius of convergence
36. ## Math calculus 2

Find the volume of the solid generated by revolving the given region about the line x=16: y=4-x,y=0,y=2,x=0.
37. ## Calculus

Use algebraic manipulations to evaluate lim x->infinity for the function. f(x)=x^2+4/x+3 Is the answer 1 or interdemediate?
38. ## Calculus

Find the interval on which the curve of ∫ 6/(1+2t+t^2) where b=0 and a=x is concave up. Heres my work but im not sure at all g '(x) = 6/(1+2x+x^2) g ''(x) = -(2+2x)/[(1+2x+x^2)^2] upward when g ''(x) > 0. - (2+2x) > 0 x < -1
39. ## Calculus

Find the derivative of the given function at the indicated point. (use f'(a)=lim [f(a+h)-f(a)]/h as h approaches 0) This is what I have so far: [1/(x+h) - 1/2]/h = [2 - (x+h)]/(h(x+h)(2)) = [2-x-h]/(h(x+h)(2)) ...and now I'm stuck. Help? Thx
40. ## Math-Calculus

Question Details: Suppose f(3)=2, f '(3)=1/2, and f '(x)> 0 and f "(x) < 0 for all x. (a) Sketch a possible graph of f (b) how many solutions does the equation f(x)=0 have? Why? (c) Is it possible that f '(2) = 1/3? Why?
41. ## integral calculus

can anyone give me a site that best explain about the topic "work" and "center of moment"... thanks... :)
42. ## Calculus

The function f is given by f(x)=3x^2+1. What is the average value of f over the closed interval [1,3]? The answer I get is 12, but the book says it's 14. I don't understand why.
43. ## calculus

Find the area of the region bounded by the graph of y^3=x^3 and the chord joining the points (-1, 1) and (8,
44. ## calculus

in your own words, describe how limits can be used to find the instantaneous rate of change of a function.
45. ## calculus

Find the derivative of (3x+17)^13 (14x+6)^11x^-4/5 / (20x +3)^-9 using logarithmic differentiation. Assume x > 0.
46. ## calculus

For each of the following limits, determine the indicated limit if it exists. lim f(x)=? x approaches 4 from the left f(x)= -3.9997
47. ## Calculus

Solve the following initial valued problems: a) g′(x) = sin(x), g(π) = 2. b) g′′(x) = 18x, g′(0) = 1 and g(0) = 5. b) g′′(x)=12x2 +2,g′(1)=7andg(1)=3.
48. ## Calculus

Given f and g are differentiable functions and f(a)=-4, g(a)=c, g(c)=10, f(c)=15 f'(a)=8, g'(a)=b, g'(c)=5, f'(c)=6 If h(x)=f(g(x)). find h'(a)? i'm not really sure how to get the answer. g'(a)=b, f'(b)=? How do i go about doing this. My reasoning must be
49. ## calculus

Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) (11)/(x^3-125) dx
50. ## calculus

Solve for all real values of x. 3tan^2x = 3^1/2 tan x I have no idea how to approach this problem.
51. ## calculus

Find the area of the region bounded by the graph of y^3=x^3 and the chord joining the points (-1, 1) and (8,4)
52. ## calculus

Find the indefinite integral and check the result by differentiation. ∫((t^3/3)+(1/4t²)dt
53. ## calculus

Find the indefinite integral and check the result by differentiation. ∫u²√(u^3+2) du

Determine the equation of the tangent line to the function f(x) = x + Sinx at x = pie

Determine the derivative of each function A1) y = e^x(Sin²x) A2) y = e²Sin²x B1) y = (x³ + 1)e^-2 B2) y = (x² + 1)e^-2 C) y = x²(theta^Sinx)
56. ## Calculus 2

The question is: n=0 E to infinity 4+sin(n)/3^n Does it converge or diverge? i'm doing this hw problem and I believe it converges according to other example? Is this the case?
57. ## calculus

find the following derivatives: f(x) = (2x+5)/(x^2-3) f'(x)= (2)*(x^2 -3)-(2x+5)*2x/(x^2-3)^2 is that correct??? f(x)= (lnx)(cos x) f'(x)= 1/x*-sinx or do i have to use the product rule?? thank you.
58. ## calculus 2

Use euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y'= -3x+y^2, y(0)=1
59. ## Calculus

Find the slope and y-intercept of the line through the point (6,2) that cuts off the least area from the first quadrant.
60. ## Calculus (AC)

Steve, you've been an amazing help. Thank you so much. This is the last question I need checked. Solve ∜82 using differentials. I got 3.00926
61. ## Calculus

f'(x)=sqrt(x)*sin(x) The first derivative of the f is given above. If f(0)=0, at what value of x does the function f attain its minimum value on the closed interval [0,10]?
62. ## Calculus

C(x)= 16sqrt(x) + (x^2)/1000 Find the production level that will minimize the average cost
63. ## Calculus

f(x)=(y+a) and b=the limit as y aproches 2+f is 1000 figure out a,y, and f I'm lost, but I need to know for our trimester final. I don't even know if it's possible.
64. ## calculus

Find an equation of the tangent line to the curve at the given point. y = sec x, (π/3, 2)
65. ## calculus

The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of . x 1 1.1 1.2 1.5 1.7 1.9 2.0 f(x) 1 3 4 6 7 8 10
66. ## calculus

determine the cubic function with 1 point of inflection and no relative minima or maxima.
67. ## Calculus II

How does one obtain cos2x = cos^2(x) - sin^2(x) by differentiating the identity sin2x = 2sinxcosx
68. ## Calculus II

Find the volume of the solid obtained by revolving the graph of $$y = 16 x\sqrt{4 - x^2}$$ over [0,2] about the y-axis.
69. ## Math Calculus 1

Have mercy! Find the volume of the solid obtained by rotating y=3+2x-x^2, x+y=3 about the y-axis.
70. ## calculus

How large does N have to be in order to approximate the integral of cos(x^2) from 0 to 1, using the Midpoint Rule, with error at most 10^(-6)?

The limit limh->0 ((sqrt1+h)-1)/h represents the derivative of some function f(x) at some number a. Find f and a. Please help!

find the lines that are (a) tangent and (b) normal to the curve at the given point x^2 + xy - y^2 = 1
73. ## calculus

For f(x) = e^cos(x) use your graphing calculator to find the number of zeros for f '(x) on the closed interval [0, 2π]. A 1 B 2 C 3 D 4
74. ## Calculus

Messed this up on my last question. Given the table below for selected values of f(x), use 6 trapezoids to estimate the value of ∫f(x)dx where a=1 b=10 x 1 3 4 6 7 9 10 f(x) 4 8 6 10 10 12 16
75. ## Calculus

Find the length of the entire perimeter of the region inside r = 16sin(theta) but outside r = 4.
76. ## Calculus

Which of the following functions grows the fastest as x goes to infinity? 3^x ln(x) e^4x x^10 I put e^4x but I thought that 3^x might have been it too. I know for sure that it is not ln(x) and x^10 because those grow much slower.
77. ## Calculus

f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1). (4 points) x 1 2 3 4 5 6 f(x) 0 3 2 1 2 0 g(x) 1 3 2 6 5 0 f '(x) 3 2 1 4 0 2
78. ## calculus 2

Use euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y'= -3x+y^2, y(0)=1
79. ## calculus

Find the equation of the tangent line to the graph of f(x)=4ln(9x+2)at the point of x-coordinate x=2.
80. ## Calculus

Find the volume of the solid obtained by rotating the region bounded by y=8x+24, y=0 about the y-axis.
81. ## AP Calculus

Find (dy/dx) for the following implicitly defined function: cos(x-2y) = 3y for the answer, i got.. dy/dx = (-sin(x-2y)) / (3-2sin(x-2y)) but i'm not sure if it's right..
82. ## calculus

suppose a price-demand function p(x) is defined implicitly by x= p^3-3p^2+200 find p'.
83. ## Calculus

Find the volume of the solid obtained by rotating the region bounded by y= x^(1/3), and y= x about the line y=1
84. ## Calculus II

the gamma function r(x) is defined by r(x)= integral from 0 to infinity of x^n-1(e^-1)dx where n>0. Use integration by parts to show that r(n+1)=nr(n).
85. ## Calculus

Use logarithmic differentiation to find the derivative of the following: y=x^x^2 x>0 Please show all steps so I can following for future understanding
86. ## Applied Calculus......

Rewrite the expression using positive exponents only. (Simplify your answer completely.) (x^3-y^3)(x^-3+y^-3)
87. ## Calculus

Use the alternate definition, lim x->a f(x)-f(a)/x-a, to determine the instantaneous rate of change of f(x)= 1/x at the point (1,1/5) a)1/5 b)-1/5 c)1/25 d)-1/25
88. ## Calculus :)

Find the volume of the solid formed by rotating the region enclosed by y=e^(3x)+2, y=0, x=0, x=0.4 about the x-axis.
89. ## Calculus

Find the global maximum and minimum values of f(t)=4t/(2+t^2) if its domain is all real numbers?
90. ## calculus

Find the instantaneous rate of change of y with respect to x when x = 15 for the function y = 5x2 − 2x
91. ## Calculus

I need help solving the integral of t * e^-3t dt I know that I have to solve using integration by parts and so I've let u=t to rid of dt and dv=e^-3t which I believe would yield -(1/3) * e^-3t as v. Am I doing this correctly? Thanks. I appreciate the help.
92. ## CALCULUS:)

The region between the graphs of x=y^2 and x=6y is rotated around the line y=6. The volume of the resulting solid is ____?
93. ## Calculus

Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.
94. ## Calculus

find all values of x for which function is differentiable. y=lnx^2 why is the answer= for all x doesn't equal 0?
95. ## calculus(differentian)

x=(6-2y²)/(1+y) differentiate with respect to y I saw this in a question here but..I don't get how the person go that answer.
96. ## calculus

find the exact arc length of the curve: y=0.5(e^x + e^-x) for 0 is less than or equal to x and x is less than or equals to ln2.
97. ## Calculus

calculate and simplify f(5+deltat)-f(5) all over delta t the model is f(t) = 7-2t+11t^2 for 3lessthanequal t lessthanequal 11
98. ## Calculus

The volume of the 3-dimensional structure formed by rotating the circle x^2 + (y-5)^2 = 1 around the x-axis can be expressed as V = a\pi^2. What is the value of a?
99. ## calculus

using tangent half substitution show that integral of sec(x)=ln(secx+tanx)
100. ## Calculus

Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.