Find a basis for the eigerspaca conesponding to the eigenvalue 12. 17 141 12 A basis for the eigenspace comsponding to A=36 (Type a vectot or list of vectors Type an integer or smplifed fraction for each matrix element Use a comma to separate answers as needed)

Q: Cives とz f(xy)= J36-9メ-す i) Find domajn and Ram ge Foy the fuclien

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A: As per the guidelines I can solve only first question

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

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A: Use the half-angle formulas to find the exact value of the trigonometric function sin 112.5°.

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A: Given data

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Q: ( sec(Inx) tan(lnx) dx

A: ∫seclnxtanlnxxdxLet u=lnx.=∫secutanudu=secu=seclnxAdd a constant to the solution=seclnx+C

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Q: Use the One-to-One Property to solve the equation for x. (Enter your answers as a comma-separated…

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

A: Let's find.

Q: d Calculate r:(t) - r2(t)] and r:(t) x r2(t)] first by differentiating [ri(t) × r2(t)] first by…

A: Given that     r1(t) = cos(t)i + sin(t)j + 8tk    r2(t) = 7i + tk

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Q: THAnUNIVERS Q3) Find the integration: S- (x+1)/x2+2X

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A: Given :

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Q: dz dz and dy dx Suppose z is a function of x and y, and tan y² + x² = z®e6y. Solve for

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A: Integral

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Q: X+3 Q4) Find the integration by using: dx J 2x3-8X

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Q: Evaluate the definite integral. e16t i + e¬tj +t k )dt O el6 – 1 (e-- - 1) + i+ (e-1 – 1) j + , k 16…

A: To solve the given integral.

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Q: 2. Find the r educed echelon form of the fo A = 0 0 0 6 54 0 (714161 Show your working

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Q: d Calculate ri(t) r2(t)] and ri(t) × r2(t)] first by differentiating d dt dt the product directly…

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Q: Determine if the following function is continuous or discontinuous at x = 0? 4z +5 f(2) = %3D 9- 32

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Q: Find f andf, and evaluate each at the given point. y' f(x, y) (6, -6) = arctan f,(6, -6) = (6, -6) =

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

A: Vector

Q: Find div F and curl F if F(x,y, z) = 9e*Y i – 8 cos yj+ 4 sin? z k. %3D div F= curl F=

A: F(x,y,z)=9e^(xy)i-8cosyj+4sin^2zk ∇F=∂F(x,y,z)∂xi+∂F(x,y,z)∂yj+∂F(x,y,z)∂zk…

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Q: 34. Which of the following is solvable directly by power rule of antiderivative? A. [xe"dx B. Ssin*…

A: Which of the following is solvable directly by power rule of antiderivative?

Q: Please answer all parts in detail.

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Q: dx (2x2+1)2

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

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Q: QI: Find dyldx for the following functions:- (3) y = (tan x)tnz+ t (4) y = sin-(x² +x) + 5"

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

A: Let's find.

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

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Q: (8x + 4x)v4x² + 8 – 24x³ – 32x If f(x) = (/4x2 + 8 - x*) then f'(x) = 4r2 +8

A: f(x) = (4x2 +8 - x2 )2 f'(x) = (24x2 +8 - 2x2)(8x/(24x2 +8)  -2x ) f'(x) = ((24x2 +8 - 2x2)(4x -…

Q: Find all points (if any) of vertical tangency for the curve represented by x = t? + 2t – 3 and y =…

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Q: +4x –1 dx x' - x 2.

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…