69 -24 A) -24 Solve lim B) 4 9+2 2-9 C) 24 D) -

Q: dy dx = 4. dt Given y= 5x +2x, find when x = -3 and dt - - dy (Simplify your answer.) dt

A: dxndt = nxn-1 .dxdt

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A: Given a differential equation.  

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A: Find your answer below 

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A: First we find slope of the function y=5x2-x dydx=10x-1dydxx=1=10(1)-1dydxx=1=10-1dydxx=1=9 At x=1, y...

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Q: Find the unit vector in the direction of v. v = -6.3i + 3.7j = n

A: Topic = Vector

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Q: If f(x) = 2 sin(x) + 3x", find f' (3). f' (3) =

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Q: x2 + x+1 x -1 Find all the asymptotes of f(x) = O No slant aymptote Horizontal asymptote y=0 Vertica...

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Q: sin (:) tan r 2. Find the derivative of f(r) = using logarithmic %3D differentiation.

A: To find the derivative of fx=sin31x tan x5π-x5e2x using logarithmic differentiation.

Q: Find the point of tangency and equation of the tangent line of the following functions given a singl...

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Q: 8. Find the volume of the region bounded by the plane z = 16 and the paraboloid z = (Use cylindrical...

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Q: Question 6 The area of a square is increasing at a constant rate of 1 cm2/sec. How fast is the diago...

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Q: 5.(y?dy) = x(xdy – ydx)ey

A: xexy(x dy-ydx)-y2 dy=0x2 exy dy -xy exy dx =y2 dyx2y2exy -xy exy dxdy =1dxdy=x2y2exy -1xyexy x=vydxd...

Q: _Show that the following are metric on R": d,(x,y) max, isn Ixi - vil : d,(x,y) E X-Yil.

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Q: Question 4 Given: f (x) = x +7 and g (x) = x² . Find the limit: lim, -3 9 (f (x)). O (E) O 18 O 12 O...

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Q: Considev the differential egn tem The companent respet to of its ganenal solutionn in given By? para...

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Q: Let f(x) = 3 cos(x) sin¬(x). Find f' (x). f'(x) =

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Q: Use Lagrange multipliers to solve the following exercise. Find three positive integers x, y, and z t...

A: f(x, y, z) =x+y+zg(x,y,z)=kxyz=8F(x, y, z, λ)=f(x,y,z)-λ(g(x,y,z)-k)F(x, y, z, λ)=x+y+z-λ(xyz-8)

Q: Let u = (-1,3) and v = (2, -5). %3D Find the component form of the vector 5u – v.

A: This question is based on resolution into vector components.

Q: Determine if the geometric series converges or diverges. If it converges, find its sum. 10 1+ 11 10 ...

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Q: Find dy/dx in terms of x and y if arctan(x*y) = y“. dy dr

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Q: In Problems 43-54, find each indefinite integral. (Check by differentiation.)

A: Given ∫(5ez+4) dz

Q: Find the angle O between the two vectors given below. 0%3(5,2)cnd v= (-6,-1). Ako drawa figure.

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Q: -u, 3v, v - u, and 2u + 5v. 3 Find (7, 6), v = (4, –4) = n 2 (a) 3 (b) 3v (c) V - u

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Q: Find the angle 0 between the vectors in radians and in degrees. u = (2, 2), v = (4, -4) %3D | (a) ra...

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Q: ecimal places.) u = i + 4j + 8k rad rad

A: We are asked to find the direction cosines

Q: dx – log(x² + y²) = eª + cot(xy). sec x

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Q: 1) Suppose that you are headed towarda plateau S0 meters high. If the angle of elevation to the top ...

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Q: tind the component form of the given vector V. belaw Dont forget round off to two decimal places. 55...

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 250 cub...

A: Solution ) volume of cylinder = 250 πr2h = 250 h = 250/πr2 Cost = 0.02( 2πrh ) + 0.02 πr2 + 0.06 πr2...

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does...

A: Given equations,x = 4t +2 y = 3z = -t+1andx = 2s+2y=2s+3z = s+1

Q: f(x) = 4x^3 − 3x^2 − 18x + 5. (e) Find the inflection points of the graph of f, if any.

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Q: | (r – 1)³ + 1, if x 2 1. Determine if g(x) = is differentiable at x = 2.

A: Checking continuity:=limx→2- g(x)=limx→2- (x-1)3+1  limx→2- g(x) =2Right hand side limit=limx→2+ g(x...

Q: The orthogonal trajectories of r = 5a sin 0 is, where a is an arbitrary constant r = csin 0 O r5 = c...

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Q: Find the magnitude (w) of u=(-8,18)

A: If the vector u =<u1,u2> then magnitude of u , u= u12+u22 .

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

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Q: Let f be a real-valued function on R. Suppose that f(−1) = 3 and f'(x) ≤ 2 for all values of x. How ...

A: f(-1)=3f'(x)≤2Integrating w.r.t x;∫ f'(x) dx ≤ ∫2 dxf(x)≤2x+Cf(-1)=33=2(-1)+CC=3+2C=5

Q: Find the solution to the following differential equation: У+ 16у %3D 0, у(0) 3 2, У (0) %3 2, У(0) 3...

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Q: 4. Find the general solution of the differential equation using the method of undetermined coefficie...

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Q: CHECK

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given ...

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Q: Find the sum of the series Σ /n+4 n = 1

A: First operate the given sum on both terms and then calculate the sum.

Q: Determine whether u and v are orthogonal, parallel, or neither. u = -4i + 15j - k v = 4i + j - k par...

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Q: S cot5xdx

A: Solve the integration

Q: If xy+Iny= x²y, compute y 2xy? +y2 y = - xy+2 – x²y O A. O B. None of the other choices OC. 2xy2-y? ...

A: We have to find y' for the given expression                                                         ...