Sinh3u= sinhu +3Coshuxsinhu= 3sinhut4sinh'u

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: z = If X – y show that: =D0

A: Given: z=xyx-y And x2∂2z∂x2-y2∂2z∂y2=0   As we know that; The Quotient rule; fg'=f'·g-g'·fg2 The…

Q: Solve for x. 7 49°

A: A triangle is a polygon having three sides and three vertices. Sum of interior angles of triangle is…

Q: Which of the following gives /₁ O 5tanh-¹ (5x) + C Otanh-¹ (5x) + C Ocoth ¹(5x) + C 5coth-¹(5x) + C…

A:

Q: exp(iz) = 1+ iV3.

A:

Q: tdt 1-t4

A: Topic = Integration

Q: solve For B, and B₂ 0 = -22 0 = = 2 2 i=1 Xii lyi - (B₁ Xii + B₂ Xiz)) x ₁₂ (y₁ - (B₁ Xi₁ + B₂ Xiz))

A: Given system of equations0=−2∑i=1nXi1(yi−(β1Xi1+β2Xi2))0=−2∑i=1nXi2(yi−(β1Xi1+β2Xi2))Which can be…

Q: Y₁' = 3Y₁ + 1/₂ ل3 Y/₂ = 2y + 2y₂

A:

Q: & lve by line x=+I and line y I

A: The integration of [(x2+xy)dx + (x2+y2)dy].

Q: 5. (1- x)"dr+ j*+x{1-x)*]dy = 0when x=2 nd y=l 6. yd-xy=y*ty

A:

Q: Qil If y , Show that y=2x- 2y3

A:

Q: Find + C

A: Given:         ∫2exdx Taking constant out.        =2∫exdx

Q: -3 0 2 1-2 1 Given C = 0 - 3 4

A:

Q: 9. Simplify sec² x - 1 sec² x

A: secx=1cosxI=sec2x-1sec2xsin2x+cos2x=1

Q: Y/9-2/5=1/3 Show also the checking

A: Solve and check the equation Y9-25=13.

Q: YA 7) 3 X+4 3 y>}x-1 2 432 -2 -1 -4 2 3 4 -2 -3 4 -5

A: The given inequality is: y≤-34x+4y>12x-1

Q: If (2,9)=, then f„- If f(x,y)

A:

Q: The height of 10 plants is measured in inches and found to be 12,6,15,3,12,621,15,18 and 12. Verify…

A: We know that, Mean, X bar = (summation Xi)/m Here n= 10 X bar = (12+6+15+3+12+6+21+15+18+12)/10 = 12

Q: if z1 = i and z2= -(3)^0.5– i find the arguments for the quotient

A:

Q: Find a natural cubic spline interpolating the data (-1, 13), (0,7), (1,9)

A: Writing data in table format x -1 0 1 y 13 7 9 Formula for natural cubic spline is:…

Q: (5, 2)

A:

Q: Suppose u = (-3,0,0) and v = (-3,-2,3). Then: u +0= u – T= | 3u= 7u – 30=

A:

Q: 5- 24 1+ A to A' type your answer. B' type your answer. and C' type your answer.

A: The given data is:   From the graph, the coordinate of A2,-3, B5,-4, and C2,-4 To find the…

Q: If ƒ (x, y) = x³y5 + 2xy, then what is the second coordinate of Vf? (Remember to use * for…

A:

Q: What is the equation for the following quadratic in the form y= ax^2 +bx +c

A: y=ax2+bx+c The given equation intercept the x axis at -3,0 and 9,0 The equation passes through 3,6…

Q: Given sin(a)= and a is in quadrant IV and sin(B) = and /2<B<. Use sum and difference formulas to…

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Q: Find A if possible. If not, write “not defined". 1 8. A= 1 6 A- ) 3 1 9. А%3 9. 3

A:

Q: form y = mx + b that repres

A: From given graph it is clear that

Q: az Find for z = e2z-y.

A: Given : z = e2x - y

Q: ifferentiate the funtion y = 2 csc (1-3x)

A: Giveny=2cosec(1-3x)Aim: dydx

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.