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Find the equation of a line parallel to x-axis and passing through the origin.
Concept: undefined >> undefined
Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, – 1), (4, 3, – 1).
Concept: undefined >> undefined
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Find the relationship between a and b so that the function f defined by f(x) = `{(ax + 1", if" x<= 3),(bx + 3", if" x > 3):}` is continuous at x = 3.
Concept: undefined >> undefined
For what value of λ is the function defined by f(x) = `{(λ(x^2 - 2x)", if" x <= 0),(4x+ 1", if" x > 0):}` continuous at x = 0? What about continuity at x = 1?
Concept: undefined >> undefined
Is the function defined by f(x) = x2 − sin x + 5 continuous at x = π?
Concept: undefined >> undefined
Discuss the continuity of the following function:
f(x) = sin x × cos x
Concept: undefined >> undefined
Discuss the continuity of the cosine, cosecant, secant and cotangent functions.
Concept: undefined >> undefined
Find the value of k so that the function f is continuous at the indicated point.
f(x) = `{((kcosx)/(pi-2x)", if" x != pi/2),(3", if" x = pi/2):}` at x = `"pi/2`
Concept: undefined >> undefined
Find the value of k so that the function f is continuous at the indicated point.
f(x) = `{(kx^2", if" x<= 2),(3", if" x > 2):}` at x = 2
Concept: undefined >> undefined
Find the value of k so that the function f is continuous at the indicated point.
f(x) = `{(kx +1", if" x<= pi),(cos x", if" x > pi):}` at x = π
Concept: undefined >> undefined
Find the value of k so that the function f is continuous at the indicated point.
f(x) = `{(kx + 1", if" x <= 5),(3x - 5", if" x > 5):}` at x = 5
Concept: undefined >> undefined
Find the values of a and b such that the function defined by f(x) = `{(5", if" x <= 2),(ax +b", if" 2 < x < 10),(21", if" x >= 10):}` is a continuous function.
Concept: undefined >> undefined
Show that the function defined by f(x) = cos (x2) is a continuous function.
Concept: undefined >> undefined
Show that the function defined by f(x) = |cos x| is a continuous function.
Concept: undefined >> undefined
Examine that sin |x| is a continuous function.
Concept: undefined >> undefined
Determine the order and degree (if defined) of the differential equation:
`(d^4y)/(dx^4) + sin(y^("')) = 0`
Concept: undefined >> undefined
Determine the order and degree (if defined) of the differential equation:
y' + 5y = 0
Concept: undefined >> undefined
Determine the order and degree (if defined) of the differential equation:
`((ds)/(dt))^4 + 3s (d^2s)/(dt^2) = 0`
Concept: undefined >> undefined
Determine the order and degree (if defined) of the differential equation:
`(d^2y)/(dx^2)^2 + cos(dy/dx) = 0`
Concept: undefined >> undefined
Determine the order and degree (if defined) of the differential equation:
`(d^2y)/(dx^2)` = cos 3x + sin 3x
Concept: undefined >> undefined
