Evaluate the limit 9х + 5 lim z+00 2r2 – 6x + 6

Q: A ball is thrown into the air and its position is given by h(t) = - 4.3t2 + 41t + 15 where h is the…

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Q: If z = 52? – 3y? + 4y, find the differential dz. You should have variables dz, dy, y, and z in your…

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Q: d. [r:(t) r2(t)] and r:(t) x r2(t)] first by differentiating d Calculate dt the product directly and…

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Q: Answer the following questions for the function f(x) = x/x? + 1 defined on the interval – 5 <x < 7.…

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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: This question can be solved using the concept of domain and of functions and value of a function at…

Q: dx 9- x 15.

A: Topic = Integration As per guidelines , At  a time only one question can be answered out of…

Q: your

A: Please refer to the image below

Q: dx 5-x?

A: We will solve the integral.

Q: completely

A: We will solve the integration.

Q: Given the equation z + 10z°y – 8y² + z* = 4 az Use implicit differentiation to find dz

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Q: Let v=f(x) be a solution of the first order linear differential equation y'=y-10x² such that f(0)…

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Q: 2. S CoSx+sinx-1

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Q: Use the formula k(t) = |r(t) × r"(t)|| ||r(t)||° to find «(t). r(t) = 8 cos(7t)i+ 8 sin(7t)j + 3tk…

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Q: dy tay +x?

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Q: dx x?(4x++9)Z

A: Integration are simplyfied..

Q: cy?t1) e COSX y2 dy 8- COSX CotX

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Q: (1) fx sin x dx

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

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Q: a) Determine whether the series 11n? + 8n + 32 is n³ + 3n2 – 7n + 1 n=1 RY convergent or divergent.

A: Since you have posted multiple questions which are not interlinked i can do first question as per…

Q: Зx* у + tan y dy Given a first order differential equation dx Q3 x' +xsec? (a) Clarify the exactness…

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Q: Find div F and curl F if F(x, y, z) = xz³i+ 4y°x²j+ 6z²yk. div F= curl F =

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Q: Find the limit of the following sequence or determine that the sequence diverges. 15 Select the…

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Q: Find div F and curl F if F(x, y, z) = 17y*z*i – 3x'2ºj – 3ry®k. div F= curl F=

A: Let's find.

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: 1. Calculate the following limits (showing all working): log,(n) + 5" n-0o log7(n) + 7" Vn5 + 2 +…

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Q: dx Half-angle Substitution cos x +sin x-1

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Q: Evaluate the following limit using Taylor series. 7 7 tan -(x) – 7x + lim 4x° 7 7 tan "(х) - 7x +-…

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Q: Find V · (V × F), if F(x, y, z) = 3e"*i+3.xe"j – 8ev²k. V ·(V × F)

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Q: Find the curvature and the radius of curvature at the stated poin r(t) = 11 cos(t)i + 10…

A: Here we have r→(t)=11cost i +10sint j +10t k  at=π2 The formula for curvature is…

Q: 1. 5x²+4x2-5 dx

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Q: Apply

A: We will solve the integration.

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A: Let's find.

Q: Find curl (3zi + 4xj+ 5yk). curl(3z i+ 4xj+ 5yk) = ( i )i + ( i )j + ( i )k

A: We will find the curl.

Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: Evaluate the definite integral. i +e´j+tk )dt O e 7 – 1 e17 - (e-' – 1) + - (e~) - 1) j + k 17 O el7…

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Q: Find r'(t). r(t) = (tan-(11t))i+t cos(t)j – Vik

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Q: Find div F and curl F if F(x, y, 2) = 17y*z*i – 3a*2®j – 3ry®k. div F= curl F=

A: Divergence of F: ∇·F=i→∂∂x+j→∂∂y+k→∂∂z.i→17y4z4-j→3x3z6-k→3xy6 ∇·F=∂∂x17y4z4+∂∂y-3x3z6+∂∂z-3xy6…

Q: Evaluate sin? xcos xdx .

A: To evaluate: ∫sin2x cos3x dx=∫sin2x cos2x cos x dx=∫sin2x (1-sin2x) cos x dx

Q: 4. x(x² – 1)² dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: dr Let A be the area of a circle with radius r. If dt dA = 2, find dt when r = 5.

A: Given :drdt=2r=5

Q: 2. S x²-6x-4 xp x+2

A: Given: I=∫x3-6x-4x+2dx As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫a·fxdx=a·∫fxdx

Q: Find the value of the following definite integrals. Show your solution. 1. L* + 4) dx 2. f(cos x +…

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Q: Find curl(6z i + 7x j+ 6y k). curl(6z i+ 7x j+ 6y k) = ( i )i + ( i )j +(i )k

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Q: partial fractions to frd use 2 |- x9 + x8 2 3

A: Using partial fraction solving the given integration.

Q: Consider the initial-value problem y" + 4y = 5 sin 3t, y(0) = 0, y' (0) = 3. %3D (a) Use the Laplace…

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Q: x + 2y = 1 , x – 2y = 8 . Credit will be given for use of the method, and not for the so y =-7/4.

A: We will solve using cramers rule.

Q: roduct directly and then by applying the formulas dr dr r(t) and dt dr, dr x ). dt Fi(t) - cos(t)i +…

A: To differentiate.

Q: S(Vcos x + sin x)´dx

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Q: 2.2 State the identity that validate sin x = 3 cos x- and hence show that 6+9/3 tan x = [10] 23

A: Follow the procedure given below.

Q: Find div F and curl F if F(x, y, z) = x*i – 11j + yzk. div F= curl F=

A: Vector