Q: 2 a) The scalar projection of a =(2, 2, 5m) on b = (0, -3, 3) is -1. Determine the value of m. L b)…

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Q: 10. Use Euler's method with h = 0.1 to approximate the solution to the initial value problem y=x-y,…

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Q: Given the function f(x)=x+3x²+4x²-3, find the intervals of concavity and the inflection points.

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Q: Use a graph off to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x…

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Q: The linear density p in a rod 3 m long is Pave 14 x + 1 Find the average density Pave (in kg/m) of…

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Q: Find the general solution for the differential equation. dy = = 12xy dx The general solution of dy…

A: dy/dx =12xy Find general solution of dy/dx = 12xy y =?

Q: Find all the critical points of the function f(x, y) = x³ + ½y³ – 9x² – 21x – y — 66 and label them…

A: fx,y=x3+13y3-9x2-21x-y-66

Q: Write the logarithmic expression log(2√7) as an expression involving two separate logarithms.

A: Given  To write the logorthemic expression for log(x^6 √y^-6)

Q: Sketch the graph of a typical function with the conditions specified below. lim f(x) = -2. lim f(x)…

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Q: A solid cylindrical cord of elastic material has length 32 inches and radius 0.5 inch. The cord is…

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Q: 1. Perform the double integration: and r = y³ in the first quadrant. 1 SS₁ (²- (x - y) dA, where D…

A: given double integration ∫∫D(x-y) dA where d is the region in the x-y plane bounded by y=x3 and x=y3…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √6-x, 4 ≤x≤6

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Q: In the following, let f and g be functions such that f' and g' are both continuous on [3,6] and both…

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Q: Find an equation y = f(x) for the parametric curve c(0) = (cos(8), 2 cos(0) + 5 sin² (0)) and…

A: We are required to: Find an equation y=f(x) for the parametric curvec(θ)=[cos(θ),2cos(θ)+5sin2(θ)]…

Q: Evaluate 5 5 625 ** 4 Jo eys dydxdz.

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Q: Evaluate the integral. Show that the substitution x = √II sec(0) transforms I into cos(0) de, and…

A: I=∫dxx2x2-11 where, x=11secθ

Q: Write the expression as a sum and/or difference of logarithms, with all variables to the first…

A: Let, y=ln6p3q5 y=ln6p3q512 Using power rule  lnak=klna .......(i) y=12ln6p3q5

Q: A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The…

A: Radius of the silo for minimum cost. *given :- cost of metal dome = 2*cost of cylindrical concrete.

Q: A hummingbird needs 10 grams of sugar and 8 grams of protein each day. One honeysuckle flower…

A: NOTE: Refresh your page if you can't see any equations. . x=number of honeysuckle flower y=number of…

Q: Solve the initial value problem. xy'+y = x² + 4, y(1) = 5

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Q: Use the Root Test to determine whether the series convergent or divergent. Σ(13) Identify an…

A: Given: ∑n=1∞n2+37n2+9n  We are required to find: If the series is convergent or divergent(using the…

Q: [ 4xex dx

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Q: Test the series for convergence or divergence using the Alternating Series Test. √n 4n+ 5 Identify b…

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Q: 2. Use the product rule to find the derivative for g(x)= (3x*-7)(2 - 5x³) and create the equation of…

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Q: Find the Taylor series at x = 0 for the function by calculating three derivatives and using the…

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Q: Write an equation (any form) for the quadratic graphed below 15

A: Given: parabola with vertex (3,3) and passes through point (1,1) To find: Equation of parabola

Q: 28. 6 S x dx 3√√x-3

A: Given integral ∫36xx - 33dx

Q: A 10 ft chain weighs 65 lb and hangs from a ceiling. Find the work done (in ft-lb) in lifting the…

A: We have to find the work done in lifting the chain.

Q: Find the largest value of that satisfies: loga (2) -log(x + 1) = 3 x -

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Q: 5 Use the linear equation y =(x- x - 32), where x is the degrees Fahrenheit and y is the degrees…

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Q: ds dt |₁=5 m/s

A: We know that the speed formula =sqrt((dx/dt)^2+(dy/dt)^2)

Q: Find for the parametric curve c(t) = (t-¹ - 6t, 2t³) at the point t = 2. dx (Use symbolic notation…

A: Given :-  Parametric curve ct=t-1-6t ,2t3 Parametric curve c(t) is represented as c(t)=(x(t),y(t))…

Q: Given the demand function D(p) = 150-3p², Find the Elasticity of Demand at a price of $6 At this…

A: We have to find the elasticity at the given price.

Q: 1 5 A 3 2 1 To find the blue shaded area above, we would calculate: [ f(x)dx = area Where: a= 1 2 3…

A: find the area of the blue shaded region . f(x) is passing through the points (2, 4) and ( 4 , 3) ,…

Q: Speedometer readings for a vehicle (in motion) at 15-second intervals are given in the table. t…

A: Consider the table

Q: Find the complex zeros of the following polynomial function. Write f in factored form. f(x)=x² +6x³…

A: Given function : f(x)=x4+6x3+2x2+54x-63

Q: Question 2: Find the slope of the tangent line of the function y = 3x² - 4x² at the point x = 12…

A: The function is y=3x32-4x12  We need slope of the tangent line at x=12   Slope of the tangent line…

Q: 1. ann- √n²-n -

A: We will simplify the given expression and try to find out limit.

Q: -In ( + C) = n u' (x) = e6x-5u

A: Use seperate the variable

Q: For the function f(x)=14x³ -x, make a table of slopes of secant lines and make a conjecture about…

A: The function fx=14x3-x

Q: Determine the convergence or divergence of the series

A: We have to find if the given series converges or diverges.   For this we will use the integral test…

Q: Use Euler's Formula to express each of the following in a + bi form. (Use symbolic notation and…

A: -e3π4i               e2πi            7ie-π3iTo find : Express in a+bi form.We know that,…

Q: Let the vector v have an initial point at (−5, 1) and a terminal point at (−8, 6). Determine the…

A: Given data The initial point of v at (-5,1) The terminal point is (-8, 6)

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 7x + 19 between x =…

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Q: T³ (x4+3) ¹ This can be transformed into a basic integral by letting Consider the indefinite…

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Q: Find the solution of the differential equation that satisfies the given initial condition. dy dx =…

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Q: Find the average value gave of the function g on the given interval. 8 1+ t²' gave = g(t) = [0, 9]

A: The function isgt=81+t2 ; 0,9

Q: 4. Trace the curve: y² = x²-4x-12 x²-2x-3

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Q: Find the scalar and vector projections of b onto a. a=3i-j+4k, b=j+k

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Q: 5. Express u = (-4, 3, —2) using the unit vectors.

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