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Chapter 12 Solutions
Calculus Early Transcendentals, Binder Ready Version
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- Determine whether the functions y, and y, are linearly dependent on the interval (0,1) y=1-2 sint, y, = 12 cos 2t Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y, = ( )y½ on (0,1), the functions are linearly dependent on (0, 1). (Simplify your answer.) O B. Since y,= ( )y½ on (0,1), the functions are linearly independent on (0,1). (Simplify your answer ). OC. Since y, is not a constant multiple of y, on (0,1), the functions are linearly independent on (0, 1) O D. Since y, is not a constant multiple of y, on (0,1), the functions are linearly dependent on (0,1).arrow_forwardDetermine whether the functions y₁ and y₂ are linearly dependent on the interval (0,1). y₁ = tan ²t-sec c²t₁ y₂ = 6 Select the correct choice below and, if necessary, fill in the answer box within your choice. © A. Since y₁ = (y₂ on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) B. 1 Y₂ on (0,1), the functions are linearly dependent on (0,1). Since y₁ = (Simplify your answer.) C. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly independent on (0,1). D. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly dependent on (0,1).arrow_forwardFind the general solution to the linear ODE. Use each method (educatedguessing) exactly once.dy/dt −2y = cos(t)arrow_forward
- Use the Chain Rule to find dw/dt. w - In (√x² + y² + x²), W = dw dt Need Help? Read It x = 6 sin(t), y = 9 cos(t), z = 8 tan(t)arrow_forwardFind a value for the constant a so that f(x) = ax² models the data. If you are uncertain about your value for a, check it by making a table of values. a = X y 1 4 2 16 3 36arrow_forwardUpload answer sheets Verify whether u = x+y+z, v = x²+y²+z², w = x³+y°+z³-3.xyz are functionally dependent, and if so, find the relation between %3D them.arrow_forward
- Select all of the following equations for which y is a function of x.arrow_forwardDetermine whether the functions y, and y, are linearly dependent on the interval (0,1). y1 =sint cos t, y, = 5 sin 2t Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y, = y, on (0,1), the functions are linearly dependent on (0,1). (Simplify your answer.) O B. Since y, =O2 on (0,1), the functions are linearly independent on (0,1) (Simplify your answer.) O C. Since y, is not a constant multiple of y, on (0,1), the functions are linearly independent on (0,1). O D. Since y, is not a constant multiple of y, on (0,1), the functions are linearly dependent on (0,1).arrow_forwardFind the characteristic equation, complementary solution, and particular solution using the method of variation of parameters.arrow_forward
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