# Pre- Calculus

21,837 results, page 96

1. ### calculus

use a sign chart to solve inequality. Express answers in interval notation. x^2+6<2x
2. ### Calculus

write and row reduce the augmented matrix to find the general solution. x + y - z = 7 2x - y - 5z = 2 -5x + 4y + 14z = 1 3x - y - 7z = 5
3. ### Calculus II

Solve the initial value problem using Taylor Series and the following conditions: y'(t) = y(t) + 2t y(0) = A
4. ### Calculus

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. y = tan x, 0 < x < π/9
5. ### Calculus Help

Find the derivative of the following function showing your work and fully simplifying your answer. f(x)=(8x-3)^5/(6x+7)^12 Thank you!!!
6. ### AP Calculus

Approximating the integral from 0 to 6 of (e^x dx) by 3 circumscribed rectangles of equal width on the x-axis yields ____. a) 2e^2 + 4e^4 + 6e^6 b) 2(e^2 + e^4 + e^6) c) 2(e + e^3 + e^5) d) e + 3e^3 + 5e^5 e) e^2 + 3e^4 + 5e^6
7. ### Calculus

If position is given by p(t)=t^2 +1, find the velocity v(t) at t = 2. I'm completely lost as to where to even start with this problem.
8. ### Calculus

At what interval is e^(-5x^2) concave up? I know the second derivative is 100x^2*e^-5x^2-10*e^-5x^2 but I just can not figure this one out. Thank you for your help!

Use a linear approximation (or differentials) to estimate the given number. (1.999)^4
10. ### 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).
11. ### Calculus

What are two conditions that must be met before the Extreme Value Theorem may be applied?
12. ### 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
13. ### Calculus Please Need Urgent2 :/

Consider the function f(x) whose second derivative is f''(x)=8x+4sin(x). If f(0)=3 and f'(0)=2, what is f(x)? f(x)=??
14. ### calculus

Compute the limit of the partial sums to determine whether the series converges or diverges. 1)6 + 4 - 4 + 4 - 4 + 4 - 4 +...
15. ### Calculus

1.a)Determine dy/dx if y= sqrt[(3x^2+2)^3] For this question, I got 9/2x(3x^2+2)^1/2 as my answer. b)State any values of x for which the function is not differentiable
16. ### calculus

find the volume of solid inside the paraboloid z=9-x^2-y^2, outside the cylinder x^2+y^2=4 and above the xy-plane

Find maxima and minima and points of inflection. f(x) = 2x^3 - 3x^2 -36x +100 on the interval [-6,4]
18. ### Calculus

Given f(x) = cubed root of x^2 (2x+5)^3, find the critical numbers after you identify the domain.
19. ### Calculus

find the extreme values of the function and where they occur y=1/(sqrt 1-x^2). So far I have y'=x/((1-x^2)(1-x^2)^(1/2)) but I am stuck.
20. ### Calculus

State the cartesian equations of two lines that make angle of 60 degrees with the line r=(1,3)+s(1,1)
21. ### Calculus-Math

Complete the table. y = f(g(x)) u = g(x) y = f(u) y = (2x − 4)^7 u = y= This problem involves the chain rule of derivatives.
22. ### Calculus-Math

f(x) = (1/2)x ln(x^6) (−1, 0) (a) Find an equation of the tangent line to the graph of f at the given point. y=
23. ### math calculus 3

find a formula for a function g( x,y,z) whose level surfaces are planes parallel to z=3x-2y+7
24. ### calculus

Find the interval [a, b] on which the function f(x) = 2 x3+3 x2−12 x+3 is decreasing. Enter your answer as: [a, b] for some constants a, b.
25. ### Calculus

Find the equation of the tangent to the curve y=3x^2+4x which makes a 45 degree angle with the negative x-axis
26. ### Calculus

Integrate sqrt(x^2 + x) dx I have completed the squares and got x^2-x = (x+1/2)^2 -1/4 Now i don't know how to proceed, plz help me!
27. ### calculus

Use iterated integral to find the area enclosed by r=2sin2(theta). How do i graph this?
28. ### calculus

How do I use the product rule to find the derivative of the following. y=(x+1)(3square root x+7) y'= Please help
29. ### Calculus

Find the equation of the line tangent to the function f(x)= square root of (x^3 + 4x) through the point (2,4)
30. ### Calculus

Find the derivative of y=xe^-x^2. Is the x being multiplied by (e^-x^2)? Product rule? I don't understand how to approach this problem.
31. ### Calculus

Find an equation of the tangent line to the graph of f(x)=xsinx when x=0. A. y=0 B. f'(x)=0 C. y=xcosx+sinx D. y=x E. None of these
32. ### Calculus

Estimate the area under the graph of f(x)= x^2 + 2 x from x=1 to x=5 using 4 approximating rectangles and left endpoints.
33. ### calculus, help!

Evaluate the definite integral: int_{1}^{e^9} \frac{dx}{x \sqrt{\ln x}} = i gt my answer as 1^(e^9) but it's saying it's wrong
34. ### Calculus

The function h(x) = x^3+bx+d has a critical point at (2,-4). Determine the constants b and d and find the equation of h(x). Show your work.
35. ### Calculus

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

y = (6x^2-6)^4/x I would appreciate it more if work was shown. Thank you (I have the answer but want to know how to do it)
37. ### Calculus

Solve without a calculator. cos(arcsin (3x/2)) I made a triangle but im stuck after that..
38. ### Calculus

Use implicit differentiation to differentiate y=x^(8/37), by writing it as y^37=x^8. Express your answer only in terms of x.
39. ### Calculus

How can I solve this using Log differentiation? I'm not sure how to even start it. y=(cos(x)(x^2+9)^(2/3)/(sqr(x^3+2))
40. ### math

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = e^(3t^2) − 3t dt from 4 to x
41. ### 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.
42. ### 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
43. ### 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.
44. ### 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
45. ### Calculus

Let f for all Real numbers, be an odd function. Explain why, for any positive number a, the integral from -a to a of f(x) = 0.
46. ### Calculus 1

Find the exact value of each expression. (a) tan(sec^−1 5) (b) sin(2sin^-1(5/13))
47. ### Calculus

Let R be the interior of the circle 4x2 + 4y2 −4x = 0. Evaluate double integral sqrt(x^2+y^2)
48. ### calculus

The position of a particle is given by the equation of motion s(t)= 1/(1+t)where t is in sec and s in meters find the velocity.
49. ### Calculus

Find the surface area of the part of the sphere x2+y2+z2=81 that lies above the cone z=√(x2+y2)
50. ### calculus

Use implicit differentiation to find the slope of the tangent line to the graph of 18*x^(1/2)+5y^(1/2)+14 at(81/324,1)
51. ### Calculus

(3) Suppose that f : R2 → R is a continuous function at x0 ∈ R2 and that |f(x0)| > 2. Show that there is a $> 0 such that |f(x)| > 2 whenever ||x − x0|| <$.
52. ### calculus 2

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

What is the derivative of f^3(g(x)) where both are continuous functions? I used chain rule and got 3f^2(g(x))f'(g(x))g'(x) but it is not right.
54. ### Calculus

Given the table below for selected values of f(x), use 6 trapezoids to estimate the value of x 1 3 4 6 7 9 10 f(x) 4 8 6 10 10 12 16
55. ### Calculus

Which of the following is the general solution of the differential equation dy/dx = 2x/y? y2 = x2 + C y2 = 2x2 + C <- my answer y2 = 4x2 + C x2 − y2 = C
56. ### Calculus

Find the specific solution of the differential equation dy/dx = 4y/x^2 with condition y(−4) = e. y= -1 - 4/x <- my answer y=-1*e^(1/x) y=e^(-4/x) None of these
57. ### Integral calculus

find the work required to pull up the anchor if the cable weighs 20 lb/ft in water
58. ### Integral calculus

find the work required to pull up the anchor if the cable weighs 20 lb/ft in water
59. ### Calculus

Determine whether the hypotheses of the Intermediate-Value Theorem are satisfied. f(x)=x^1/3 , [a,b]=[-1,1] Please, explain. Thank you.
60. ### mathematics-calculus-derivatives

. Try this. If y=cosx find dy/d5x please show workings #thanks
61. ### Calculus

Evaluate as limit approaches 0. (Without using l'hopital's rule. ( Sqrt(4+sin(x))-2 ) / (3x)
62. ### calculus sir damon help me or steve

integrate dx/root(coshx-1) plz show step
63. ### Calculus

Find the absolute maximum and minimum values of the function f(x)=3(x-2)^(2/3)+5 on the interval [1,10]? I'm not sure how to do this. Please help.
64. ### Calculus AB

Without using a calculator, what is the exact value of sec(arctan(12/5)) - sin(arccot(3/4))
65. ### Calculus AB

One of the equal angles of an isosceles triangle is 55 degrees. If the base is 20 cm, what is the perimeter and the area?
66. ### Calculus1

find the derivative using fundamental theorem of calculus integral of sin^3tdt from e^x to 0
67. ### 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
68. ### calculus

Find all first and second partial derivatives of z with respect to x and y if x^2+4y^2+16z^2−64=0.
69. ### calculus need help

If 3ay^2=x(x-a)^2 with a>0, prove that the radius of curvature at the point (3a, 2a) is 50a/3. Help with working plz
70. ### Calculus

Construct a function f : R 2 ¡æ R such that its saddle points are given by {(n, 2m+1−n)|n ¡ô Z, m ¡ô Z}, where Z is the set of integers.
71. ### Calculus

Find the volume of the solid under the plane 3x + 3y − z = 0 and above the region bounded by y = x and y = x^4
72. ### Calculus

I need help determining whether the following functions are even, odd, or neither. Please help me. 1. f(x)=4x+5 2. f(x)=x^3-x-2 3. f(x)=x^4-x / x^5-x 4. f(x)= x^3-x / x^5
73. ### Calculus - Special sum formulas

Find the formula of n Σ (j+3)(j-4) j=1 I have gotten to n(n+1)(2n+1)/6 - n(n+1)/2 - 12n How do I simplify it from there?
74. ### Calculus

Given 4∫8 (4 on top, 8 on bottom) f(x)dx= 12 and 4∫8 g(x)dx= 5. Evaluate the following: 4∫8 [2f(x)-3g(x)]dx Would I just put 12 in for f(c) and 5 in for g(x) then solve?
75. ### calculus

Find the domain of the vector-valued function. r(t) = sin ti + 4 costj + tk plz help me working
76. ### Calculus

Find all values of c that satisfy the Mean Value Theorem for integrals for f(x)= x^{2} on the interval [-3, 3]
77. ### 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)]
78. ### 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:
79. ### Calculus

What would the smallest positive integer be for n if: y=sinx and y^(n) means the nth derivative of y with respect to x.
80. ### calculus

A rectangle has an area of A. Find the dimensions that minimize the perimeter. Show that it really is a minimum.
81. ### Calculus

What is the largest possible product of two non-negative number whose sum is 1
82. ### Calculus

Piecewise function x if −2≤x≤0; x^2 if −2<x<0; 8-x. If if −2≤x≤3; (d) Write down an analytic formula for f^{-1}, and state its domain and range.
83. ### Calculus

Let F(x) = (x+1) / (x^2-16). Use the definition of the derivative to compute f'(x) and give its domain. Show all steps.
84. ### Calculus

For which values of x does the curve Y= (3x^3-3x^2+1) / (2x^2-1) , have a horizontal tangent? Show steps or explain, i dont get it

Simplify the cubed root of 432x to the 12th power
86. ### Calculus - Derivatives

Use implicit differentiation to find the second derivative y'' of the function given. x^2 + 5y^3 = 8
87. ### calculus

Find the derivative of (3x+17)^13 (14x+6)^11x^-4/5 / (20x +3)^-9 using logarithmic differentiation. Assume x > 0.
88. ### 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.
89. ### calculus

Find the exact area of the surface obtained by rotating the curve about the x-axis. y=((x^3)/4)+(1/3X), 1/2≤X≤1

Find the range of the function F(x)= definite integral from [-6,x] of sqrt(36-t^2)dt. [0, 36π] [0, 18π]*** [-6, 6] [-6, 0]
91. ### calculus

Find the constant a such that the function is continuous on the entire real line g(x)=x^2-a^2/x-a if x doesn't equal a 6 if x=a
92. ### CAlculus

Find the linear function satisfying the given conditions. g(2) = 9 and the graph of g is perpendicular to the line 4x − 2y = 3. g(x) =
93. ### Calculus

How do you find the original function given the equation of a tangent line and two points?
94. ### Calculus 2

Determine the first three terms of the power series representations for the following functions: a) 2/(1+x)^3 b) 1/1+x^2 c) ln(1+x)
95. ### Calculus

Find the length of the parabola y^2=4ax cut off the line x=a about the x-axis
96. ### Calculus

Show that volume of the solid generated by revolving y=1/x between x=1,2x=infinity about x-axis
97. ### calculus

Express the following as a product containing only sines and/or cosines. sin9x−sin7x
98. ### Calculus 2

The region between the graphs of y=x^2 and y=6x is rotated around the line x=8. The volume of the resulting solid is?
99. ### 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
100. ### AP Calculus Help

The position of a particle is given by r(t)=(t+cos(t/2), -3sint). What is the particles velocity vector when t=pi? a)v=<0.5, -3> b)v=<2, -3> c)v=<0.5, 3> d)v=<1.5, 3> e)v=<2, 3> Thank you so much!!