Find the limit. lim væ+1

Q: (3) (3) (4) h. y = sin(x² + 1) i. y = 3e4x5 j. y = In√5x3+4

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

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Q: (f) If F(x, y) = 5y sin(xy)i + 5x sin(xy)j, f(x, y) =

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Q: The linear density in a rod 8 meters long is 13/√x+1 kg/m, where x is measured in meters from one…

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Q: Using rectangles each of whose height is given by the value of the function at the midpoint of the…

A: The objective of the question is evaluate the area by help of midpoint rule.

Q: The estimated marginal profit associated with producing x widgets is given by P'(x) = -0.6x + 24…

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Q: Calculate the integral, assuming that fo f(x) dx = -4, ² f(x) dx = 4, ₁ f(x) dx = 11. (Use symbolic…

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Q: 1. Use the delta method, 2 BONUS MARKS y = 5x² dy dx = lim h-0 f(x+h)-f(x) h to find dx for the…

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Q: Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the…

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Q: Choose the expression that completes the following equation so that it is an identity. tanx+cotr = O…

A: Given,  tan(x)+cot(x)=sin(x)cos(x)+cos(x)sin(x)                        =sin2(x)+cos2(x)cos(x).sin(x)…

Q: Given u = and V = , find 2u + 3v. O a) Ob) Oc) Od)

A: Given,  u=4,-3v=-1,2 Let's compute  2u=24,-32u=<8,-6> and  3v=3-1,23v=<-3,6>

Q: The cost dollars, for a video game developer to code g games can be represented by the function vig)…

A: The cost, in dollars, for a video game developer to code g games can be represented by the function…

Q: .) Use method of Laplace Transforms. y"-6y +13y=0, y(0) = 1, y (0) = -3.

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Q: 3. Find the total derivative of V with respect to X. V=3X³ +5Y²+6Z Z=4+5X Y=3X+6Z+5XZ

A: Given, V=3X3+5Y2+6ZZ=4+5XY=3X+6Z+5XZ

Q: Find the limits. f(x) = x + 2 g(x) = x² (a) lim_ f(x) = (b) (c) X-5 lim g(x) = X-0 lim g(f(x)) =

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Q: Question 1 of 20 o f(x) O View Policies Current Attempt in Progress Find a formula for a rational…

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Q: b) [ Find the volume of the solid obtained by rotating the region bounded by the curve about the…

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Q: A factory has in stock 300 kg of a certain material, which is sold to the customers in 10 kg…

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Q: what

A: Please refer to the image below

Q: Solve the given differential equation subject to the indicated conditions. y" - 4y = x + sin x, y(0)…

A: The given differential equation is y''-4y=x+sin x, y0=5, y'0=2y

Q: Find the absolute minimum and absolute maximum values off on the given interval. f(t)=t√ 25-t²,…

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Q: 9. Let f(x) = 10 z+12 2 10 For each of the following limits involving f, either evaluate the limit…

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Q: 6. A solid is bounded by the surfaces z = 4 and z= √√x² + y² . Find the exact value of the volume of…

A: To find the volume.

Q: Find the limit. Ilm (x + 7)

A: We can find the limit as below.

Q: question b

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Q: Find the area of the region enclosed by the functions. y=x* and y=x The area of the region enclosed…

A: Area between the curve

Q: Consider the function f(x, y) = xy² exp xp ( - 1/3² + y) Compute the stationary points of the…

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Q: (a) Find the equation of the tangent line to the curve y = x² at x = 1. (b) The line in part (a) is…

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Q: Evaluate the limit. lim X→∞ 5 (₁ + 2/2 + 1/2)² X

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Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve r(t)…

A: This question can be solved using the concept of vectors and derivatives.

Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then…

A: A detailed solution is given below.

Q: nd all the critical points of the function f(x)= ={ x² 23 if x<1 if x ≥ 1

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Q: Find an explicit solution of the given initial-value problem. dy 12-13 y(4) = 4 dx

A: The given differential equation is dydx=y2-1x2-1 and y(4)=4We have to find the explicit solution of…

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 4z2 = 21,    (−3,…

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Q: Given the following functions, use function composition to determine if f(x) and g(x) are inverse…

A: This is a function problem

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3 + 6x3/2…

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Q: Wind forces F (N/m) exerted per meter of building side as a function of vertical distance y (m) from…

A: We have to find the net force.

Q: Find the linear approximation L(x) of the function f(x) = (1-x)1/2 at a=0 and then use L(x) to…

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Q: Sketch the plane curve. r(t) = tr + t2j, [01] y 1.0 0.8 0.6 0.4 0.2 y 1.0 0.8 0.6 0.4 0.2 0.2 0.2…

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Q: The estimated marginal profit associated with producing x widgets is given by P'(x) = -0.6x + 24…

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Q: If y=2x²-4, what is its inverse? or Oy¹--√2 Dy^--, DOIN such that xs-4 such that x2-4 such that x20…

A: Given, y=2x2-4 To find the inverse, we need to swap the variables 'x' &amp; 'y' x=2y2-4 Now solve…

Q: If f ' ' ( x ) = 2 , then f ( x ) is concave up at x = 2 . True OR False

A: f(x) is concave up at x= k if f"(k)&gt;0

Q: n n2 + 1 Σ;

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Q: 7. Find the greatest integer that divides all numbers of the form 109" +96" - 53″ – 66″ for n ≥ 1.…

A: Disclaimer: Since you have asked the multiple question,we will solve the first question for you. if…

Q: If an = n²(n+5n²) 4n4-n²+1' then by using the Nth term test for divergence, the series Σ an…

A: We have to find if given series converges or diverges.

Q: Find the indicated particular solution of the differential equation. dy dx + 7y= -2e - ⁹x; x = 0…

A: Topic = Differential equation

Q: Find the first three nonzero terms of the Maclaurin expansion of the function. f(x) = 3e -2x

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Q: 3 X The double integral ³ x dydx has a rectangular region. Select one: True False

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Q: Use the Laplace transform to solve the given initial-value problem. y' + 6y=e³, y(0) = 2 Step 1 To…

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Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1,1) in the direction of from the…

A: We have to find the directional derivative.