Find the limit (if it exists) (а) lim x — 5 (b) lim 5 x-243 x2 + 6x + 8 (c) lim x--2 x + 2 sin x (d) lim 2→0 2+ Vx Vx + 4 – 2 (e) lim sin(7x) (f) lim 3x (g) lim tan x

Q: у? — 4у — 21 Зу2 — 17у — 28 imy→7

A: Given query is to find the limit of the expression.

Q: dy tay +x?

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Q: り (2xy+y?) dx - 2x? dy = o 2) Yy dx - (メ+ 2y)? dy -0

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Q: 31) Find two sets af poler Coorelinates for tue pornt (0,-4) Jer OLQL2T Auywers's 37 テノ, (16,…

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Q: Find V. (F x G), if F(x, y, z) = 14.ci + j+ 13yk and G(x, y, z) = xi + yj – zk. V· (F × G) :

A: Vector

Q: 3) use implict differentiation to finol dd et the point (8.1). 4 xy+ slny=32 Anywery: 28 a) 37 り 36…

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Q: 9. Let A be the coefficient matrix for the system of linear equations: 2x + 9y – 5z = 1, — 6х — 2у +…

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Q: Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 3yz²k; (2,…

A: This question is based on divergence of vector.

Q: 9. (D² - 1)y = 2/(e – e-*).

A:

Q: Find the absolute maximum and minimum values of the function on the given curve. Function: f(x. y) =…

A: Let's find.

Q: Use the Rules of Differentiation to differentiate the following functions: a. f(x) = 2x³+ 6x d. h(x)…

A: Given data

Q: Q2) Find the integral of: 6 tan*x dx

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Q: Find V · (V × F) if F(x, y, z) = 2 sin xi+ 8 cos(4.x – 5y)j + 2zk. %3D - V·(V × F) = %3D

A: Given :F(x,y,z)=2 sin xi+8 cos(4x-5y)j+2zkTo find : ∇·(∇×F)

Q: X1 + 2x2 + x3 = 12 X1 – 2x2 + x3 = 0 X1 + x2 – x3 = -1 Solve the following system using Gauss-…

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Q: dy for x'e*y Find dx sin' ( 3x) + In (y) by using implicit differentiation.

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Evaluate the definite integral. i+e'j+t k )dt ell (e-l – 1) + (ell – 1) i – (e-1 – 1) j +, k 11 ell…

A: Given: I=∫01e11t i+e-t j+t kdt   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: Find the curvature and the radius of curvature at the point t = 0. I = e' cos(t), y = e' sin(t), z =…

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Q: 6. Find equations of the tangent line and the normal line to the curve y = 1+ x2 at the point (1,)…

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Q: Find r'(t). r(t) = (tan¬(2t))i+t cos(t)j – vtk NOTE: Enter your answer in terms of i, j, and k.…

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Q: Find V. (V x F) if F(x, y, z) = 4 sin xi + 7 cos(8x – 9y)j+ 9zk. V·(V × F)

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Q: Q2 Evauate : fx V+1 dx

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Q: (-1) ntl n=1 n3

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Q: Evaluate the following integrals. 2 (a) S(csce)(1 + sin´e + sine cot + sin¯0 + sin0 cot¯0 ´e)de

A: Solution is given below:

Q: Find V· (V x F) if F(x, y, z) = 2 sin xi + 2 cos(8x – 9y)j+ zk. - V · (V × F) :

A:

Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given problem:- r(t)=cos(πt)i-ln(t)j+√(t-6)k ,t0 =7 find domain of r(t)and r(7)

Q: Find the general solution of the given variable separable egm atim. dy *+ ay? (2) %3D

A: Given :dydx=e3x2+4y2

Q: We want to fenca in a ne slide b up againd a lacae building and Idbesn't noedh fancing rechanguler…

A: This question can be solved using the concept of maxima or minima.

Q: Consider the function f(x)=−3x2+30x−2.   a.   ​Determine, without​ graphing, whether the function…

A: Given; f(x)=-3x^2+30x-2

Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: 33) Find tue ared ef tue Serface formed by revolving thecirele r= f10) = 10 C6s Q f10) =10 Cos Q…

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Q: y = Vx + 3 from x=1 to x=4

A: We find the area under given curve and bounded by axis and given lines x=1 & x=4 using definite…

Q: what is the exact answer

A: The exact answer was the second last line of the original solution.  So, the exact answer is:…

Q: Q2: Solve the following integrals:- (1) fx² sin x dx (2) f dx 4x2- xp: (3)f x sin(x + 1)dx

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Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt' the product directly…

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Q: v F= F=

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Q: Find [r(t) · u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = ti + 8t2j + t³k, _u(t) =…

A:

Q: 9) use the snell metnod to sef up end eveluete tueinteyrel tret gives the volume of the solid…

A: Using shell method, volume is evaluated.

Q: Q5) Find the integration by using (by part method): Se3x sin X dX

A:

Q: x² Consider the function f(x) = x² –1 (a) Find the intercepts of the graph of f (if any). (b) Find…

A: This is a problem related to function calculation. Based on the general formula and concept we will…

Q: Find r'(t). r(t) = (tan(10t))i+t cos(t)j – VEk NOTE: Enter your answer in terms of i, j, and k.…

A: Given problem :- r(t) =(tan-1(10t)) i+t cos(t) j-√tk Find:- r'(t)

Q: 1. The approximate value of -31.8 using linear approximation O -2.0025 O None of the choices O…

A: Ni

Q: Find V x (V x F) if F(x, y, z) = 2:xy j+ 9xyz k. V x (V × F)

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Q: y=x 2 y = x+1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: dx ²+8x-9

A: Given: ∫dxx2+8x−9 Let I = ∫dxx2+8x−9 ⇒I = ∫dxx2+9x-x−9

Q: For ​f(x)=x+5 and ​g(x)=3x+1​, find the following functions.   a. (f◦g)(x)​; b. (g◦f)(x)​; c.…

A: Topic = Functions

Q: Q1) Determine if the following integrals converge or diverge. If the integral converges determine…

A: Given query is to find integral converges or diverges.

Q: ; Test the following series whether it is convergent or divergent (show all your works) n2 +7 a) 2…

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Q: S (1/(X(Im)*) dx X(Inx)

A: LetI=∫1xlnx2dxLet u=ln(x)differentiate 1xdx=duI=∫1xlnx2dx.I=∫1u2du.I=∫u-2duUse power…