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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

Determine the following indefinite integrals. Check your work by differentiation. 3 / ( 2²/1 + 2 - 3/3) dx 4 2 X
Evaluate the following limits. x" lim x1 x 1 1 n is a positive integer
Determine the following indefinite integrals. Check your work by differentiation. Jo (4z1/3 - z-1/³) dz
Evaluate the following limits. lim x→3 v-1-√₂²-5 V-3 V
Use linear approximations to estimate the following quantities. Choose a value of a to produce a small error.1/3√510
Evaluate the following limits. y² + y - 6 V8-y²-y 2 lim y-2
Determine the following indefinite integrals. Check your work by differentiation. 2 √√r² dr [V
Determine the following indefinite integrals. Check your work by differentiation. 1218 t 13 | - dt
Evaluate the following limits. x² 4x + 4 lim x-2 sin² (7x)
Determine the following indefinite integrals. Check your work by differentiation. 4x4 X 6x² -dx
Find the intervals on which f is increasing and decreasing.ƒ(x) = tan-1 x
Evaluate the following limits. lim 3 4x³2x² + 6 3 TX³ + 4
Evaluate the following limits. lim x-2 √3x + 2-2 x 2
Determine the following indefinite integrals. Check your work by differentiation. [(₁ ¹7) di dt sin 4t sin-
Evaluate the following limits. 3x4 – x² 2 lim x→ 6x4 + 12
Determine the following indefinite integrals. Check your work by differentiation. [(s (sin 2y + cos 3y) dy
Evaluate the following limits. tan x lim X→π/23/(2x - π)
Evaluate the following limits. lim x →∞ e3x 3e³x + 5
Determine the following indefinite integrals. Check your work by differentiation. [2 2 sec² 2v dv
Determine the following indefinite integrals. Check your work by differentiation. [(s (sec² x - 1) dx
Evaluate the following limits. In (3x + 5e*) In (7x + 3e²x) lim x→∞ In
Determine the following indefinite integrals. Check your work by differentiation. sin - 1 cos²0 - dᎾ
Evaluate the following limits. In (3x + 5) lim x In (7x + 3) + 1 →∞⁰
Determine the following indefinite integrals. Check your work by differentiation. [(s (sec² 0 + sec 0 tan 0) de
Determine the following indefinite integrals. Check your work by differentiation. (31²+ sec² 21)dt
Evaluate the following limits. Use l’Hôpital’s Rule when needed. lim csc x sinx x-0
Evaluate the following limits. lim X→∞0 x² - In 2 (2/x) 3x² + 2x
Consider the following functions and express the relationship between a small change in x and the corresponding change in y in the form dy = f' (x) dx. f(x) = 3x³ - 4x
Limits Evaluate the following limits. Use l’Hôpital’s Rule when needed. lim xx-00 In³ x √x
Evaluate the following limits. 2 tan x lim x→/2 sec²x
Determine the following indefinite integrals. Check your work by differentiation. Іся csc 3Ф cot 3Ф do
Evaluate the following limits. lim x csc x x-0
Determine the following indefinite integrals. Check your work by differentiation. √₁ 3 4 + v² 2 av
Evaluate the following limits. Use l’Hôpital’s Rule when needed. [ - x X x+1 (: © lim In
Evaluate the following limits. lim x-0+ cotx X
Evaluate the following integrals. S 10V Vx dx
Evaluate the following integrals. et 4e + 6 Sz dx
Evaluate the following integrals. L Þei dx 2 x ln x
Evaluate the following integrals. x + 4 x² + 8x + 25 2 13 dx
Evaluate the following integrals. dx √x²-9 2 =,x > 3
Evaluate the following integrals. In 3 In 2 coth x dx
Evaluate the following integrals analytically. dx √4- 2 X'
Evaluate the following integrals. ex Ve²x + 4 2x =dx
Evaluate the following integrals. x² X S Jo 9-x6 dx
Evaluate the following integrals analytically. dy y²√9-y² 2 S
Evaluate the following integrals or state that they diverge. +2 Lov dx 2√4-x²
Evaluate the following integrals analytically. dx √9x² V9x² - 25 X V 5 3
Evaluate the following integrals or state that they diverge. • m/2 sec Ꮎ dᎾ
Evaluate the following integrals analytically. 0 √3/2 x² (1-x²)3/2 dx
Evaluate the following integrals analytically. 0 √3/2 4 -dx 9 + 4x²
Evaluate the following integrals analytically. (1 1 - u²) 5/² -du u 8
Evaluate the following integrals analytically. [si sinh' x dx
Evaluate the following integrals analytically. se sech² x sinh x dx
Use the reduction formulas in a table of integrals to evaluate the following integrals. Stan tan* 3y dy
Evaluate the following integrals. dx -2 X x² - 2x + 10
Evaluate the following integrals analytically. x² cosh x dx
Evaluate the following integrals analytically. In(√3+2) 0 cosh x dx V4 - sinh² x
A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined bywhere we assume that s is a
Evaluate the following integrals analytically. x² 2 dx 2x 15
Use numerical methods or a calculator to approximate the following integrals as closely as possible. St In x 1 + x dx TT² 12
Evaluate the following integrals analytically. x ³ 3 dx - 2x²
Let Use any method you choose to find a good approximation to I. You may use the facts that I = x² - x 2 St -dx. In x 0
Evaluate the following integrals analytically. - dy 2 (y + 1)(y² + + 1)
A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined bywhere we assume that s is a
A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined bywhere we assume that s is a
A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined bywhere we assume that s is a
A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined bywhere we assume that s is a
Solve the following initial value problems. y' (t) = 1 + e', y(0) = 4
Evaluate the following improper integrals (Putnam Exam, 1939). 3 dx dx 2. S₁ √(x-1)(3-2) D² S₁ (²+1²+1 ed- a. b. ex+1 +e³-x 1
Solve the following initial value problems. y"(t) = 12t - 20t³, y(0) = 1, y'(0) = 0
Consider the tank problem in Example 6. For the following parameter values, find the water height function. Then determine the approximate time at which the tank is first empty and graph the
Solve the following initial value problems. y' (t) = sint + cos: sin t + cos 2t, y(0) = 4
Solve the following initial value problems. 0 = (1) *_x - x = (x), α
Consider the tank problem in Example 6. For the following parameter values, find the water height function. Then determine the approximate time at which the tank is first empty and graph the
Solve the following initial value problems. y'(x) = 4 sec² 2x, y(0) = 8
Find the general solution of the following differential equations. y' (t) = tlnt + 1
Solve the following initial value problems. 4e²-8e-2x, u(0) = 1, u'(0) = 3 u"(x) = 4e²x =
Find the solution of the following initial value problems. y' (t) = te', y(0) = -1
Find the solution of the following initial value problems. u'(x) = 1 2 x² + 16 4, u(0) = 2
Find the general solution of the following differential equations. u'(x) 2(x - 1) 2 x² + 4
Verify that the given function y is a solution of the differential equation that follows it. Assume that C is an arbitrary constant. y(t) = Ce; y'(t) + 5y(t) = 0
Find the general solution of the following differential equations. v' (t) 4 1² - 4
Find the general solution of the following differential equations. y"(x) = X (1-x²)³/2
Verify that the given function is a solution of the differential equation that follows it. u(t) = C₁e¹ + C₂te¹; u"(t) - 2u' (t) + u(t) = 0
Verify that the given function is a solution of the differential equation that follows it. g(x) = C₁e-2x + C₂xe-2x + 2; g"(x) + 4g'(x) + 4g(x) = 8
Find the solution of the following initial value problems. p'(x) = 2 x² + - P(1) = 0 x²
Verify that the given function is a solution of the differential equation that follows it. u(t) = C₁t² + C₂t³; tu"(t) - 4tu' (t) + 6u(t) = 0
Find the solution of the following initial value problems. y"(t) = tet, y(0) = 0, y'(0) = 1
Verify that the given function is a solution of the differential equation that follows it. u(t) = C₁t5+ C₂t4 - 1³; t²u"(t) - 20u(t) = 14t³
Verify that the given function is a solution of the differential equation that follows it. u(t) = Cel/(4¹); u' (t) + - u(t) = 0
Verify that the given function is a solution of the differential equation that follows it. z(t) = C₁e + C₂e²t + Cze-3t - e¹; z."(t) + 2z"(t) - 5z'(t) — 6z(t) = 8e¹
Evaluate the following integrals analytically. Sta tan u du
Evaluate the following integrals or state that they diverge. S In x² dx
Evaluate the following integrals analytically. 7/6 sin Ꮎ dᎾ
Evaluate the following integrals or state that they diverge. 1 11 dx (x - 3)²/3
Evaluate the following integrals or state that they diverge. [₁3 X 2 x² + 2x + 1 - dx
Evaluate the following integrals analytically. π/2 cos+ x dx
Evaluate the following integrals or state that they diverge. 0 10 dx 10- x
Evaluate the following integrals analytically. S sec5 z tan z dz
Evaluate the following integrals or state that they diverge. 8 S₁²= dx x-1

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