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Q: If x is divisible by 5 or y is divisible by 5, then xy is divisible by 5.
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Q: 1. [e²y ycos (xy)] dx + [2xe²y xcos (xy) + 2y] dy = = = 0
A: According to guidelines I can only solve first question ,rest can be reposted.
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Q: Let f(x) be a function defined on [0,1], such that f(0) = 0 and f(1) = 1 . Which of the following…
A: Option (1) and (2) are correct
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A: Topic = Functions
Q: Question Let h(x) = f(g(x)). If g(5) = −3, g'(5) = −4, f(-3) −4, ƒ(−3) = −1, and f'(-3) = -5, find…
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Q: 1. Among 200 people, 150 either swim or jog or both. If 85 swim and 60 swim and jog, how many jog?
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A: Find the true statement.
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Q: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at…
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Q: A rectangle is inscribed in an ellipse given by the equation x^2/49+y^2/196=1. If (x,y) is a vertex…
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Q: Consider f(x) = − 5x(8 − x)¾ Determine the intervals on which f is concave down. Of is concave down…
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Q: Given f(x) = 7x² + 4x +9, determine the value of con (-6, 6) guaranteed by the Mean Value Theorem. =…
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Q: Consider the differential equation y'' + 6y' +9y = 0.
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Q: Consider the function f(x) = (x - 1)1/3 .(a) Compute the slope of the secant lines between (1,0) and…
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Q: I. The daily temparature high can be modelled by the formula T(t) = 57.5 22.5 cos(2πt) where T is…
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- Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?You are now allowed to assume that the half-planes determined by the line with the equation ax+by +c = 0 correspond to the points (x, y) so that ax + by + c < 0 and ax + by + c > 0, respectively. Usingthis, show that axiom B4(i) holds. (Hint. Suppose (q, r) and (s, t) are on the same side of the given lineand that (s, t) and (u, v) are on the same side of the given line. en construct the parametrized linethrough (q, r) and (u, v). Consider the mappingλ γ7→ a(q − qλ + uλ) + b(r − rλ + vλ) + c and note that it is continuous and either increasing or decreasing. Use this fact to show that, for everyλ, γ(λ) > 0 or γ(λ) < 0, depending on which half-plane the points are on.)what equation is perpinduclar to x+z=1, and x+2y+4z=8 and has a point on yz plane
- Find a parametrisation of the curve of intersection of the surfaces: x^2 + 2y^2 + z^2 = 5 and x^2 + y^2 = 1 which lies in the first octantCalculate ∫C y2 dx -yz2 dy - sen(z)dz, where C is the path connecting the point A(−2,2,4) to the point B(1,2,2) by the parable z=x2 on the plan y=2A point moves along the curve of intersection of the paraboloid z=x^2+5y^2 and the plane x=3. At what rate is z changing with y when the point is at (3,-1,14)?
- Suppose the temperature at the point (x, y, z) on the sphere x2 + y2 + ?2 = 16 is T= 800xy2z3 . Locate the lowest and highest temperatures on the sphere.Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T = 400xyz2. Locate the highest and lowest temperatures on the sphere.At what point on the paraboloid y= x^2 +z^2is the tangentplane parallel to the plane x+2y+3z=1 ?
- Find the orthogonal trajectories on the sphere x2 + y2 + z2 = a2 of its intersection with theparaboloids xy = CzConsider two spheres, defined by x^2 + y^2 + z^2 = 1 and (x − 2)^2 + (y − 6)^2 + (z − 3)^2 = 16, respectively. How close are the spheres from touching?Show that the value of ∮C xy2 dx + (x2y + 2x) dy around any square depends only on the area of the square and not on its location in the plane.