EX2 Compute the secand erder partial Jerivative Fx ち,ち~ and a)

Q: Evaluate the improper iterated integral. x2 dy dx 1 + y2

A: Given: I=∫03∫0∞ x21+y2dydx As we know that; ∫11+x2dx=tan-1x+C And ∫a·fxdx=a·∫fxdx, where a is…

Q: Find the limit. NOTE: Enter the answer using round brackets. t? + 7 lim t 612 + 7't 1° = (?, ?)

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Q: Evaluate sin 5x) lim, 0 (sin 5z ) 3x O 1 O 3/5 O 5/3

A: Topic:- limit calculus

Q: Find the arc length of the parametric curve. 4 cos(t), y = 4 sin(t), z = 3t; 0<t<T L=

A: Here we have to find the arc length of the parametric curve.

Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

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Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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Q: Solve the initial value problemy-10y +50v-0 for y(0)-1 andy (0)-5. After getting the equation for…

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Q: Given y = (x + 1)(x + 2)² Find: y O (z + 2)(3x – 4) O (2 – x)(3x – 4) - O (x – 2)(3x + 4) O (2 +…

A: Apply the product rule of differentiation f·g'=f'·g+f·g' to find the derivative of the given…

Q: Find the area of the region enclosed by the parabolas y=x and y=2x-x². Make a sketch and shade in…

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Q: 1 T/2 3t/2 -1 - -2 + -3 + -4 - -5 The graph of the function f(x) = sec x is given above for the…

A: Topic:- function and calculus

Q: Given that lim f(x) = 9 lim g(x) = -4 x 2 lim h(x) = 0, find each limit, if it exists. (If an answer…

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Q: Use Riemann Sums to calculate the area under the curve over the interval (1,3] for f(x) = x² + 2

A: By using Reimann Sums to calculate the area under the curve over the interval 1, 3 for fx=x2+2.

Q: Given the vectors A = 3i – 5j + 2k and B = 7i + j – 2k. Find the vector projection of A onto B.

A: Given : A→=3i-5j+2kB→=7i+j-2k     To Find : Vctor Projection of A→  onto B→

Q: dx Ух — 12

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Q: Which among the choices is NOT true about the continuity of f(x)? if x 1 X, メ, 2 f(x) = (2 – x), O…

A: Solution

Q: d²y of the following equation then simplify whenever possible. 3) Find and dx dx- x = 3em y = 4e-m

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Q: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ),v(PR), and v(PS) respectively 31…

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Q: Find V x (V x F) if F(x, y, z) = 2xy j+ 6xyz k. %3D V × (V × F) =

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+2z²yk. %3D div F= curl F=

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Q: Verify Green's Theorem by evaluating both integrals y? dx + x² dy Ne dA ду ax for the given path. C:…

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Q: Find the area bounded by the curves y=sin x and y= cos x from x =0 tox= 7. Make a sketch and shade…

A: The region bounded by the curves y=sinx and y=cosx from x=0 to x=π

Q: Find the dimensions of a rectangle with a maximum perimeter that can be inscribed in the ellipse 4x…

A: Given ellipse 4x2+9y2=36                -&gt;Equation(1)Let (x,y) be the upper right corner of the…

Q: 8. c d 12 10 values of the areas bounded by the curve h', the derivative of h, and the x-axis on the…

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Q: 5 4 3 1 T1/2 3π/2 -1 -2 -3 + -4 -5 The graph of the function f(x) = cot x is given above for the…

A: Solution is given below:

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: Here,  a→(t)=3t i^+6 sin(t)j^+cos(2t)k^⇒v→(t)=∫3t i^+6 sin(t)j^+cos(2t)k^dt⇒v→(t)=3t22 i^+6…

Q: Determine the vector field of F Flr, y) = yl – x)

A: Solution is given below:

Q: 2x f(x) 1< x < 3 to + 5 lim n → 00 i = 1

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Q: Find the symmetric equations of the line that passes through the points (-2, 1, 0) and (1, 3, 5).

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Q: Given the function f(x) = x2 and the closed interval [0, 1, which of the following is a value of c…

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Q: Find curl (8z i + 9x j+ 8y k). curl (8z i + 9x j + 8y k) i )i + ( i )j + ( i )k

A: Given that,     8z i+9x j+8y k

Q: 2) Find and of the following equation then simplify whenever possible. dx x = 1+ Sin t y = Cos? t

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Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 s t < 1. dy

A: Given: I=∫Cx+3y2dy And x=4t, y=8t  and 0≤t≤1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: Determine whether the improper integral diverges or converges. In x converges O diverges Evaluate…

A: Here we have to determine whether the given improper integral diverges or converges.

Q: Which type of discontinuity does the function S4- a², In x, x < 1 f(x) = 1<x < e has at x 1?

A: We need to choose correct option.

Q: Solve the initial value problem y′′−6y′+9y=0 for y(0)=1 and y′(0)=3. After getting the particular…

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Q: 8* – 2* 10. lim, »0 4x

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Q: n-1 (-3)' is convergent or divergent. If it's convergent, b) Determine whether the series 4" n=1…

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Q: "I INAICATE If THtE fOLLUWINh SRRZES ConveilCE OR DeveRしe。エ0ENTICY Tésrs Uszo. TESTS HT in (4nt -n)…

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Q: Consider the matrix 2 -1 A =| 1 3 -1 -2 2

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Q: complex form and COS U+ i sin o) be the polar form Idition and subtraction between two complex…

A: Topic:- complex number algebra

Q: Find the norm (or length) of v = <-2, 3)

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Matching Type. Match the functions in Column A with their corresponding derivatives in Column B.…

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Q: 2D² +3D– 2)y = 0

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Q: ?

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Q: Use the limit definition to find the derivative of f (x), this means no short cut rules, f(x) = x? –…

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Q: 6) Find the linear approximation to R(t) = VE at t=32 Use the linear approximation to approximate…

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Q: 16. What is the derivative of f(x) = eBx+3? a. f'(x) = e® b. f'(x) = 3e®x c. f'(x) = 8e d. f'(x) =…

A: 16. fx=e8x+317. y=34x18. fx=x3-3x2-3

Q: Find the arc length L of the graph of r(t). r(t) = 5 cos(t)i + 5 sin(t)j + tk, 0<t< 2n L =

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