Vector Calculus — Page 1 — Tinkutara Math Forum

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11. If (√5) = 2.236 and (√(10)) = 3.162 then the value of ((15)/( (√(10))+(√(20))+(√(40))−(√5)−(√(80)))) is (a) 5.398 (b) 4.398 (c) 3.398 (d) 6.398 12. If x=(((√3)+1)/3) then x^3 +(1/(x^3 ))=? (a) ((28(√3) +15)/8) (b) ((28(√3)−15)/8) (c) ((27(√3)−35)/4) (d) ((27(√3)+35)/4) 13. Simplify ((x^4 ((x^3_ ((x^2 (√x)))^(1/3) ))^(1/4) ))^(1/5) (a) x^((23)/(24)) (b) x^((23)/6) (c) x^(5/6) (d) x^((119)/(120)) 14. ((3+2(√5))/(4−2(√5)))=p+q(√5) where p and q are rational numbers then values of p and q respectively are (a) −8 −(7/2) (b) 8 −(7/2) (c) 4 7 (d) −4 −7 16. 2.6^− − 0.8^− 2^− is equal to (a) ((181)/(999)) (b) ((82)/(99)) (c) ((182)/(99)) (d_(If) ) Non of these 17. If x=3(√5)+2(√2) and y=3(√5)−2(√2) then the value of (x^2 −y^2 )^2 is (a) 5760

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lim_(x→+∞) ^3 (√(x+1)) −^3 (√x) =^? 0

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a^⇀ ,b^⇀ ls the unit vector,∣a^⇀ +b^⇀ ∣=1 ask ∣a^⇀ −b^⇀ ∣?

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if f(x)=^a x=x^x^x^⋰^x (there are a x′s;a∈N and a≠0) ∫f(x)dx=?

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Question 210554

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n_0 =((Z^2 .p.(1−p))/C^(2m) )

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Question 207712

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Question 205673

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f(x)=(1/((x−1)^(ln((2/4))) )) Domain f(x) =?

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Let A ∈ R^(N×N) be a symmetric positive definite matrix and b ∈ R^N a vector. If x ∈ R^N , evaluate the integral Z(A,b) = ∫e^(−(1/2)x^T Ax + b^T x) dx as a function of A and b.

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Question 201947

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(((14)/(15)))^6 ×(((45)/(28)))^6 =

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A ball lies on the function z=xy at the point (1,2,2). Find the point in the xy−plane where the ball will touch it. Calculus 2 problem.

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Question 196918

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Prove that ∫^( +∞) _( i) (cos2t+isin2t)e^(−t^2 ) dt= ((√π)/(2e))

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Question 193204

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Question 192024

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Question 192023

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Question 191104

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Question 190006

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Question 186323

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Question 185190

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If the area enclosed between the curves y=x² and the line y = 2x is rotated round the x-axis through 4 right angles, find the volume of the solid generated

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∫_0 ^( 1) e^a a^n da=? n≥1 n∈N

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Question #181678

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Question 179453

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Question 179053

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Question #177039

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We know that vertex form of parabola is given as y = a(x−h)^2 +k From the given diagram of bridge that resembles a parabola, we have a vertex points of (0, 30) and other points due to towers that supports the parabolic−shape cable, which is (200, 150). ∴ y = a(x−0)^2 +30 = ax^2 +30 To find the value of ′a′, let′s use the given points other than vertex 150 = a(200)^2 + 30 150−30 = 40000a a = ((120)/(40,000)) = (3/(1000)) ∴ y = ((3x^2 )/(1000)) +30 Also, since we′re asked to find a function that gives a length of metal rod needed relative to its distance from the midpoint of the bridge, with each rods have an equal distance to each other, then we must consider another variable ′d′ that represents the equal distance of metal rods relative to its decided quantity and variable ′n′ given as positive integer that divides the distance of midpoint to tower. d = ((200)/n) ⇒ nd = 200 Example: Engineers decided to use 8 metal rodus, then we have d = ((200)/8) = 25 To calculate the length of each rods, let′s use the formula above First rod: y = ((3(0∙25)^2 )/(1000)) +30 = 30 ft. Second rod: y = ((3(1∙25)^2 )/(1000)) +30 = 31.875 ft. Third rod: y = ((3(2∙25)^2 )/(1000)) +30 = 37.5 ft. Fourth rod: y = ((3(3∙25)^2 )/(1000)) +30 = 46.875 ft.

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The plane y=1 slices the surface z=arctan(((x+y)/(1−xy))) in a curve C. Find the slope of the tangent line to C at x=2

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Question 164187

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Question 163914

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If f(z) = z sin(z) + ∣z∣^2 , verify if f(z) satisfy cauchy rieman condition

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Question 152597

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sin(x)=a, a∈

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(Level - 2) 10th maths assignment of polynomials by PP sir Defind upwards and downwards parabolas.

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State the asymptotes of the curve y^2 = ((3x^2 )/(x−4))

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Question 144783

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Question 137627

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What is the volume of tetrahedron ABCD, whose vertices have the coordinates A (2, 3, 6), B (3, 2, 2), C (3, 4, 7) and D (5, 1, 8). Find the lateral surface area of the tetrahedron and find the volume of the tetrahedron?