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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

Use limit methods to determine which of the two given functions grows faster, or state that they have comparable growth rates. In x; ln (In x)
Determine the following indefinite integrals. x² = 2√x + 2 X x² dx
Find the solution of the following initial value problems. p'(t) = 10et; p(0) = 100
Determine the following indefinite integrals. -#)/ 2 x5/2 dx
Find the solution of the following initial value problems. f'(u) = 4(cos usin 2u); f(π/6) = 0
Use limit methods to determine which of the two given functions grows faster, or state that they have comparable growth rates. x² In x; ln² x
Find the solution of the following initial value problems. h' (t) = 6 sin 3t; h(π/6) = 6
Determine the following indefinite integrals. x + 1 X -dx
Find the solution of the following initial value problems. 7=(x-7); 8(1) g'(x) = 7x = 2
Determine the following indefinite integrals. [12 (2x + 1)²dx
Forms evaluate the following limits or explain why they do not exist. Check your results by graphing. lim x-0¹ 3 3x + 2 3 1/x • 2x) ¹/**
Forms evaluate the following limits or explain why they do not exist. Check your results by graphing. lim (x + cos x) ¹/x X-0
Make a complete graph of the following functions. If an interval is not specified, graph the function on its domain. Use analytical methods and a graphing utility together in a complementary way.
Find the solution of the following initial value problems. g'(x) = 7x64x³ + 12; g(1) = 24
Find the solution of the following initial value problems. f'(x) = 2x 3; f(0) = 4
Determine the following indefinite integrals. [(x² (x8 - 3x³ + 1) dx
Make a complete graph of the following functions. If an interval is not specified, graph the function on its domain. Use analytical methods and a graphing utility together in a complementary way.
Forms evaluate the following limits or explain why they do not exist. Check your results by graphing. lim 1 + 2-0 10 2 Z
Make a complete graph of the following functions. If an interval is not specified, graph the function on its domain. Use analytical methods and a graphing utility together in a complementary way.
Forms evaluate the following limits or explain why they do not exist. Check your results by graphing. lim (tan x)* X-0+
For the following functions f, find the antiderivative F that satisfies the given condition. f(0) = 2 sin 20 - 4 cos 40; F TT 4 = 2
Find the function with the following properties. h'(x) = sin²x and h(1) = 1
Determine the following indefinite integrals. dx V1 - x²
Use limit methods to determine which of the two given functions grows faster, or state that they have comparable growth rates. x*; (x/2)*
Find the function with the following properties. f'(x) 3x² 1 and f(0) = 10
Find the function with the following properties. f'(t) = sint + 2t and f(0) = 5
Determine the following indefinite integrals. dx x² + 1 2
Determine the following indefinite integrals. 1+tan 0 sec 0 do
Find the function with the following properties. g' (t) = 1² + t2 and g(1) = 1
Determine the following indefinite integrals. [ (√x³ + √x³) dx
Use analytical methods to evaluate the following limits. lim (√x-2-√x - 4) X→∞0
Use analytical methods to evaluate the following limits. lim x³ 3 X-∞ X ²-) -sin-
Use analytical methods to evaluate the following limits. tan 3t lim 1/2¹ sec 5t
Use analytical methods to evaluate the following limits. lim x→+ x-1 1 Vx 1. -
Use analytical methods to evaluate the following limits. lim (7 x→π/2 2x) tan x
Use analytical methods to evaluate the following limits. lim x-0 sin x X 1/22²
Use analytical methods to evaluate the following limits. lim (x²e¹/x-x²-x)
Determine the following indefinite integrals. Check your work by differentiation. "e2re-2x 2 - dx
Use analytical methods to evaluate the following limits. lim (log₂x log3x) x →∞
Determine the following indefinite integrals. Check your work by differentiation. (√x² + √x³) dx
Determine the following indefinite integrals. Check your work by differentiation. (4 cos (4 cos 4w - 3 sin 3w) dw
Determine the following indefinite integrals. Check your work by differentiation. (csc² 0 + 1) de
Determine the following indefinite integrals. Check your work by differentiation. (csc²0+20230) de
Evaluate d/dx (3x).
Find the area of the surface generated when the given curve is revolved about the x-axis. y = 12-3x on [1,3]
Find the area of the surface generated when the given curve is revolved about the x-axis. y = 8√x on [9,20]
Evaluate the following derivatives. d dx (In (In x))
Evaluate the following derivatives. d dx امر الاداء - (x In (x)) x=|
Is x12 an even or odd function? Is sin x2 an even or odd function?
Find the arc length of the following curves on the given interval by integrating with respect to x. у= X3/2 3 x¹/2; [4,16]
Evaluate the following derivatives. d dx (sin (In x))
Evaluate ∫ 4x dx.
Find the area of the surface generated when the given curve is revolved about the x-axis. y = x³ on [0, 1]
Express 3x, xπ, and xsin x using the base e.
Find the arc length of the following curves on the given interval by integrating with respect to x. y || E 4 -12 8x2 [1,2]
Find the area of the surface generated when the given curve is revolved about the x-axis. y = x³/2 x1/2 3 on [1,2]
Evaluate the following derivatives. d dx ((In 2x)-5)
Find the area of the surface generated when the given curve is revolved about the x-axis. = = √ (e²r + e-2r) on [-2,2]
Evaluate the following derivatives. P xp -(In (cos²x))
Find the arc length of the following curves on the given interval by integrating with respect to x. 1/2: [1,9] - wek = K
Evaluate the following derivatives. d dx (In³ (3x² + 2))
Find the area of the surface generated when the given curve is revolved about the x-axis. y = √4x + 6 on [0, 5]
Find the area of the surface generated when the given curve is revolved about the x-axis. y || x ³ 3 1 4x on 2 2
Find the area of the surface generated when the given curve is revolved about the x-axis. √5x - x² on [1,4] y = √5x
Find the area of the surface generated when the given curve is revolved about the x-axis. y || 8 1 4x² 2 + on [1,2]
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. y = 8, y = 2x + 2, x = 0, and x =
Find the mass of the following thin bars with the given density function. p(x) = [x² if 0 ≤ x ≤ 1 x(2-x) if 1 < x≤ 2
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. y = 4 x, y = 2, and x = 0 YA - 4 2 0 y =
Evaluate the following integrals. Include absolute values only when needed. e dx x ln³ x
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. y = x, y = 2 x, and y = 0
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. x = 4 y + y 3¹. X = y 1 √3+ and y =
a. Write and simplify the integral that gives the arc length of the following curves on the given interval.b. If necessary, use technology to evaluate or approximate the integral. y = 4x - x²; [0, 4]
Evaluate the following integrals. Include absolute values only when needed. 0 ¹x In* (x² + 1) x² + 1 dx
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. x = y², x = 4, and y = 0
Find the area of the surface generated when the given curve is revolved about the y-axis. y || x2 4 for 2 ≤ x ≤ 4
a. Write and simplify the integral that gives the arc length of the following curves on the given interval.b. If necessary, use technology to evaluate or approximate the integral. y 1 x² + 1' [-5,5]
Devise the exponential growth function that fits the given data; then answer the accompanying questions. Be sure to identify the reference point (t = 0) and units of time.The population of Clark
Evaluate the following integrals. 0 2 4 xe x/2 dư dx
a. Write and simplify the integral that gives the arc length of the following curves on the given interval.b. If necessary, use technology to evaluate or approximate the integral. y = = [1,10] X
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. = y², x = 0, and y = 3
Evaluate the following integrals. esin.x sec x dx
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. y = x³, y = 8, and x = 0
Devise the exponential growth function that fits the given data; then answer the accompanying questions. Be sure to identify the reference point (t = 0) and units of time.Between 2005 and 2010, the
Evaluate the following integrals. S e-x/2 2 ex/2 + 1 dx
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. y = Vsin ¹ x, y = Vπ/2, and x = 0
Evaluate the following integrals. √x feve dx
Evaluate the following integrals. ex + ex et - e dx
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. y = 2x ³/2, y = 2, y = 16, and x = 0
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. y = Vcos¹x, in the first quadrant
Find the arc length of the following curves by integrating with respect to y. x = y4 4 1 8y2¹ for 1 ≤ y ≤ 2
Use the method of your choice to determine the area of the surface generated when the following curves are revolved about the indicated axis. y = 9x²/3 x4/3 32 for 1 ≤x≤ 8; about the x-axis
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. y = √50 - 2x², in the first quadrant
Evaluate the following integrals. TT/2 4sin x cos x dx
Evaluate the following integrals. In 3 In 2 et + ex e2x 2+e-2x dx
Evaluate the following integrals. 2 La (1 + In x)x* dx
Evaluate the following integrals. x² 6x² +8 dx
Evaluate the following integrals. L 10* dx
Evaluate the following integrals. 1/2 1/3 10%x dx x²
Evaluate the following integrals. 4cotr sin²x Sm dx
Evaluate the derivatives of the following functions. f(x) = (2x) 4x

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