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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

Evaluate the derivatives of the following functions. h(x) = 2(x²)
Evaluate the derivatives of the following functions. f(x) = x 77
Evaluate the derivatives of the following functions. h(t) = (sin t) Vi
Evaluate the derivatives of the following functions. H(x) = (x + 1)²x
Evaluate the derivatives of the following functions. p(x) = x-lnx
Evaluate the derivatives of the following functions. ,sin y G(y) = y sin
Let R be the region bounded by y = x2, x = 1, and y = 0. Use the shell method to find the volume of the solid generated when R is revolved about the following lines.x = -2
Evaluate the derivatives of the following functions. Q(t) = t¹/t
Let R be the region bounded by y = x2, x = 1, and y = 0. Use the shell method to find the volume of the solid generated when R is revolved about the following lines.x = 2
Let R be the region bounded by y = x2, x = 1, and y = 0. Use the shell method to find the volume of the solid generated when R is revolved about the following lines.y = -2
Let R be the region bounded by y = x2, x = 1, and y = 0. Use the shell method to find the volume of the solid generated when R is revolved about the following lines.y = 2
Use either the washer or shell method to find the volume of the solid that is generated when the region in the first quadrant bounded by y = x2, y = 4, and x = 0 is revolved about the following
Use either the washer or shell method to find the volume of the solid that is generated when the region in the first quadrant bounded by y = x2, y = 4, and x = 0 is revolved about the following
Compute the following derivatives using the method of your choice. d 4 (x²r) dx
Compute the following derivatives using the method of your choice. d dx - (e-10x²)
Compute the following derivatives using the method of your choice. [(0)]
The burning of fossil fuels releases greenhouse gases into the atmosphere. In 1995, the United States emitted about 1.4 billion tons of carbon into the atmosphere, nearly one-fourth of the world
Compute the following derivatives using the method of your choice. d dx (x-tan x)
Compute the following derivatives using the method of your choice. d dx -(x² + e*)
Compute the following derivatives using the method of your choice. d dx 1 + 4)*
Use either the washer or shell method to find the volume of the solid that is generated when the region in the first quadrant bounded by y = x2, y = 4, and x = 0 is revolved about the following lines.
Compute the following derivatives using the method of your choice. dx (ort)-x) - P
Compute the following derivatives using the method of your choice. d dx (cos (x² sin x))
Evaluate the following integrals. S." 2sin x cos x dx
Evaluate the following integrals. x²10¹² dx
Evaluate the following integrals. 2e 3ln.x X - dx
Evaluate the following integrals. 1.²0 (In x)5 x dx
Evaluate the following integrals. In²x + 2 ln x - 1 X dx
Evaluate the following integrals. pln 2 e 3x 0 e-3x dx e³x + e-3x
Evaluate the following integrals. sin (In x) 4x dx
Evaluate the following integrals. ¹16* 42x S 0 dx
Without evaluating integrals, explain why the following equalities are true. 8 # [ (8 - 2x)2² dx = 2π [ ³ (4-2) dy a. π •L(25 b. (25 (x² + 1)²) dx = 2 -2, y Vy-Toy dy
Determine the following indefinite integrals. Check your work by differentiation. + √x dx x
Determine the following indefinite integrals. Check your work by differentiation. ^2 + x² 1 + x² dx
Verify the following indefinite integrals by differentiation. These integrals are derived in later chapters. [x²0 x² cos x³ dx = 1/1/₁ sin x³ + C
Determine the following indefinite integrals. Check your work by differentiation. *1 + √x X - dx
Verify the following indefinite integrals by differentiation. These integrals are derived in later chapters. X (x² − 1)² dx = . 1 2(x² - 1) + C
If f is an odd function, why is a Sa f(x) dx = 0?
Use geometry to evaluate SV8x - x² dx.
Use the limit definition of the definite integral with right Riemann sums and a regular partionto evaluate the following definite integrals. Use the Fundamental Theorem of Calculus to check your
Show that xx grows faster than bx as x → ∞ , for b > 1.
Use the limit definition of the definite integral with right Riemann sums and a regular partionto evaluate the following definite integrals. Use the Fundamental Theorem of Calculus to check your
Use the identities sin2 x = (1 - cos 2x)/2 and cos2 x = 1(1 + cos 2x)/2 to find ∫ sin2 x dx and ∫ cos2 x dx.
Use the limit definition of the definite integral with right Riemann sums and a regular partionto evaluate the following definite integrals. Use the Fundamental Theorem of Calculus to check your
Use the limit definition of the definite integral with right Riemann sums and a regular partionto evaluate the following definite integrals. Use the Fundamental Theorem of Calculus to check your
Use symmetry to evaluate the following integrals. L -2 x⁹ dx
Explain what net area means.
Use Table 5.4 to rewriteas the sum of two integrals.Data from in Table 5.4 Si(2x³4x) dx
Use symmetry to evaluate the following integrals. 200 2x³ dx J-200
How do you interpret geometrically the definite integral of a function that changes sign on the interval of integration?
Evaluatewhere a and b are constants. b d af (1) f(t) dt and- d f d dx dx f(t) dt,
Use symmetry to evaluate the following integrals. TT/4 -π/4 cos x dx
Use symmetry to evaluate the following integrals. L₂ (3x³ -2 (3x8 - 2) dx
Use symmetry to evaluate the following integrals. TT/2 5 sin x dx -π/2
Find ∫ cos2 x dx.
Use symmetry to evaluate the following integrals. 2 L(x² − 3x² + 2x (.x.9 -2 3x5+2x²10) dx
Evaluate the following integrals. -2 (3x4 - 2x + 1) dx
Use symmetry to evaluate the following integrals. TT/4 -π/4 sin³ x dx
Use symmetry to evaluate the following integrals. 10 LO X -10 V200 x² dx
Use symmetry to evaluate the following integrals. •π/2 -π/2 (cos 2x + cos x sin x - 3 sin x5) dx
Use symmetry to evaluate the following integrals. Lo (1 − x) dx -1
Evaluate the following integrals. .2 [²(x 0 (x + 1)³ dx
Use symmetry to evaluate the following integrals. Draw a figure to interpret your result. 77 sin x dx
Evaluate the following integrals. Sc 0 21 (4x²1 - 2x¹6 + 2x¹6+1) dx
Use symmetry to evaluate the following integrals. Draw a figure to interpret your result. 2π cos x dx
Evaluate the following integrals. [(9x8 (9x8 - 7x) dx
Use symmetry to evaluate the following integrals. Draw a figure to interpret your result. 2π7 0 sin x dx
Use symmetry to evaluate the following integrals. Draw a figure to interpret your result. 77 S 0 cos x dx
Use a change of variables to find the following indefinite integrals. Check your work by differentiation. *(√x + 1)² 2√x - dx
Evaluate the following integrals. Let -2 e4x+8 dx
Use a change of variables to find the following indefinite integrals. Check your work by differentiation. 1₁ 1 10x - 3 dx
Use a change of variables to find the following indefinite integrals. Check your work by differentiation. [(x² (x² + x)¹0 (2x + 1) dx
Evaluate the following integrals. 2 x² .3 x³ + 27 S -dx
Evaluate the following integrals. [√x (√x + 1) dx 0
Find the average value of the following functions on the given interval. Draw a graph of the function and indicate the average value. f(x) = x² + 1; [-2,2]
Find the average value of the following functions on the given interval. Draw a graph of the function and indicate the average value. 1 = x² + + 7² (-1,1] 1 f(x) =
Use a change of variables to find the following indefinite integrals. Check your work by differentiation. [sin' sin ¹00 cos 0 de Ꮎ
Use a change of variables to find the following indefinite integrals. Check your work by differentiation. [x³(x+ x³(x4 + 16)6 dx
Evaluate the following integrals. [y² (3y³ + 1)² dy
Evaluate the following integrals. S dx V4 - x²
Use geometry (not Riemann sums) to evaluate the following definite integrals. Sketch a graph of the integrand, show the region in question, and interpret your result. 0 4 (8 - 2x) dx
Use a change of variables to find the following indefinite integrals. Check your work by differentiation. dx V1 - 9x²
Find the average value of the following functions on the given interval. Draw a graph of the function and indicate the average value. f(x) = cos 2x; [-]
Find the average value of the following functions on the given interval. Draw a graph of the function and indicate the average value. f(x) = 1/x; [1, e]
Use a change of variables to find the following indefinite integrals. Check your work by differentiation. [x³ sin x² sin x ¹0 dx
Evaluate the following integrals. x sin x² cos8 x² dx
Evaluate the following integrals. 3 X o dx √25-20
Evaluate the following integrals. I sin sin ²50 de 2
Find the average value of the following functions on the given interval. Draw a graph of the function and indicate the average value. f(x)= e2x [0, In 2]
Find the average value of the following functions on the given interval. Draw a graph of the function and indicate the average value. f(x) = cos x; [22-]
Evaluate the following integrals using the Fundamental Theorem of Calculus. 2 S 0 4x³ dx
Use a change of variables to find the following indefinite integrals. Check your work by differentiation. √(x6- (x63x²)4 (x5 - x) dx
Use a change of variables to find the following indefinite integrals. Check your work by differentiation. X 12 x-2 dx
Approximate the area of the region bounded by the graph of f(x) = 100 - x2 and the x-axis on [0, 10] with n = 5 subintervals. Use the midpoint of each sub interval to determine the height of each
Evaluate the following integrals using the Fundamental Theorem of Calculus. 0 2 (3x² + 2x)dx
Evaluate the following integrals. 77 L (1 - cos² 30) de 0
Find the average value of the following functions on the given interval. Draw a graph of the function and indicate the average value. f(x) = x(1x); [0, 1]
Evaluate the following integrals using the Fundamental Theorem of Calculus. 슬! 2 X dx
Evaluate the following integrals. In 2 ex 1 + ²x - dx
Evaluate the following integrals. x² + 2x .3 x³ + 3x² 2 -dx 6x

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