. Evaluate the limit of a function using the concept of Special Limits. et-1 t2-3t+5 + t2-1 1. lim t

Q: Consider the following. u = -7i - 2j - 4k, v = 4j + 4k (a) Find the projection of u onto v. i- 3j -…

A: Given, u=-7i-2j-4k v=4j+4k We know that projection of u on v is…

Q: Evaluate the integral: 5x/8x² – 1 dx - 5 (8x2 – 1)- + C (8a? – 1)-+ C (822 – 1) + C -(8x2 – 1) + C 8…

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Q: Determine whether u and v are orthogonal, parallel, or neither. u = (2, 18) 3 v = 6 O parallel O…

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Q: Let F(x) = f(x) + g(x)e*+h(x)e2x+ C be the antiderivative of G(x) =(x+ e")* Determine the value of…

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Q: nt Use the model A=Pe" or where A is the future value of P dollars invested at interest rate r…

A: Given A=P(1+rn)nt

Q: Directions: Determine whether the given functions is continuous, differentiable, neither, or both at…

A: d.According to graph of d. at x=0limx→0-dx=limx→0+dx=limx→0dx=finite.So, function is continuous. at…

Q: The integral expression J xcos (2x)dx can be evaluated using integration by parts of the form…

A: This is a problem of integration. Based on the uv formula we will solve the question.

Q: Find the equation of the tangent line to the curve y = 6 sec a – 12 cos a at the point (, 6).…

A: To find the equation of tangent for the given function.

Q: sin x e" dx Cos x

A: To evaluate the given integral.

Q: The integral of the given function f- (9- dr Arcsin +C b.+ Arcsin + C c. -- Arcsin +c d. None of the…

A: To find the value of a given integral we use the substitution method

Q: 2. An jet travels horizontally at a speed of 500mph at an altitude of 3 miles above the ground. A…

A: We need to find rate of change of angle of elevation.

Q: sin x e" dx Cos x

A: Given:       ∫sinxcosxex dx       =∫tanx exdx Integration by parts Formula:       ∫u dv=uv-∫v du

Q: A particle travels along the x-axis such that its position is given by æ(t) t22 sin (2t). What is…

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Q: Find the general solution of'the following differential equation. + 13y+ 42y 0 NOTE: Use C, and cg…

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Q: If f(x, y) = (17x - y)3, then is given by: af dy (17x (17 – ) 13 - 18 (17x 13 - - 13 Y)2 – ) 18 (17x…

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Q: Determine the limit of the sequence or show that the sequence diverges by using the appropriate…

A: an=7n2+n+24n2-3limn→∞an=limn→∞7n2+n+24n2-3           =∞∞(indeterminate form)…

Q: Water is running out of a conical funnel at the rate of 1 in3/sec. If the radius of the base of the…

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Q: By using substitution, show that x = 4 pi / 6 is a solution to the equation sin (2x) = cos (x). Show…

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Q: A closed rectangular box is to have a square base and a volume of 40 ft3. y Letting x denote the…

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Q: the following functions. Simplify, if possible. 1. g(x) = 2x3 + 6x – 2 2. h(x) = (3x + 2)² x2 3.…

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Q: Find the solution of the initial value problem 9y"-10y'+y = 0, y(0) = 9, y(0) Then determine the…

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Q: Determine the value of C in on the antiderivative of F(x)= sin (x)cos³(x) for x = 0.701 and y = 1.5.…

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Q: 5. For the Parametric curve x = a(t – sint), y = a(1 – cost) where 'a' is a constant. Find y d?y at…

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Q: Suppose that P dollars in principal is invested for t years at the given interest rates with…

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Q: 5. In the given differential equation, eliminate the arbitrary constant. SHOW YOUR COMPLETE AND…

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Q: C' (x) = – 0.02x + 30, where x represents the level of production andC'(x) represents the marginal…

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Q: -3a 36)-216 3- 2 3p x²-e3x. 時le). ex² =e12

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Q: f(x)=3x2-12x+5 and the closed interval [3,0] Which of the following is the absolute maximum and…

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Q: b. Find all solutions, if any exist, by using Gauss – Jordan reduction method.

A: Follow the procedure given below.

Q: dy dr * = 1+ ev-z+5 e + e®+y

A: Option -3:C=x e-5-ex-ydifferentiating w.r.t. x;0=x (0) + e-5(1) +exe-ydydx                -ex-y0…

Q: Let F(x) = f(x) + g(x)e* + h(x)e2x+C be the antiderivative of G(x) = (x+ e*)", Determine the value…

A: This can be solved as follows:

Q: Find an equation of the plane with the given characteristics. The plane passes through the point (6,…

A: General equation of a plane passing through a point P(p,q,r) is given by,…

Q: Find the critical numbers and absolute extrema for y on the interval [0.5, 2]. Type DNE if an answer…

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Q: 2) x" = (Power RUle, n any nonzero integer)

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Q: f(x)=3x2-12x+15 and the closed interval [3,0]. What is the critical value of f? a. x=2  b. x=4…

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Q: Let F(x) = f(x) + g(x)e* + h(x)e2x + C be the antiderivative of G(x) = (x + e*)*, Determine the…

A: The given function,  Gx=x+ex2

Q: 4. j(x) = x² secx 5. k(x) = 9x"/3 + 2

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Q: Sketch the region enclosed by the given curves and find its area. 1 y x > 0 y = x y 4 | || |8

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Q: Determine the value of the arbitrary constant of the antriderivative of F(x) = x<In(x) given the…

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Q: -x2 + 5 2. y = cos 2x³

A: Given: y=-x2+5cos2x3

Q: A student must select 6 subjects. In how many ways can he do that if there are 13 subjects and 1 is…

A: This question is from principal of counting.

Q: Determine the value of the arbitrary constant of the antriderivative of F(x) = x²In(x) given the…

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Q: (ii) Find the following indefinite integrals: 1 (a) dx (b) dx 5 - x* xe* ! dx (c)

A: A)I=∫ 1x3+1x3 dxI=∫ x-3 dx + ∫ x-13 dxI=x-3+1-3+1 +x-13+1-13+1 +CI=-12x2+3 x232 +CI=32x23 -12x2+C

Q: velocity v of a freefalling skydiver is well modeled by the differential equation m dv/dt = mg −…

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Q: 2n tan h 3x 3-) Arc sin tanh X

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Q: Use linear approximation to estimate the following quantity. Choose a value of a to produce a small…

A: The objective of the question is evaluate the value.

Q: discussed under Bernoulli Equations dy 2y dr

A: dydx=2yx-x2y2dydx-2yx=-x2y2the above eq is of the form dydx+P(x)y= Q(x) ynP(x)=-2x, Q(x)=-x2 , n=2IF…

Q: I Evaluate the following expressions by basic integration: dx 2. ,(x + 3)(x – 4)dx

A: Given

Q: - y = V1 – sinx

A: Given,y=1-sinx3y=1-sin(x)13Differentiate w.r.t. x using chain…

Q: Give all solutions of the nonlinear system of equations, including those with nonreal complex…

A: y= x2 +4x  ....(1)2x-y=-8 ......(2)2x -[x2+4x] =-82x -x2 -4x…