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Q: x² – 1 lim x→1 /x – 1

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Q: If L{f(t)} = F(s) then df -f(0) + sF(s) dt d² dt2 - f'(0) – sf(0) + s²F(s)

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

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Q: Question- Let R be the region bounded by y= x+2, y30, and x=3. Then draw the region and evaluate the…

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Q: Moha Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y x and %3D y = x2.

A: The objective of the question is evaluate the given integral.

Q: 1. S(5x4 + 2x – 1)dx 2. S dx. 3. 늘e-ndx 4. S cot?x dx In 4x 5. S A dx

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Q: d d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

A: Here we use the concept of dot product and cross product of vectors

Q: Determine the speed along a parameterized path s(t) = (9t³, 7t²) at time t = 6 (assume units of…

A: Given problem Determine the speed along a parameterized path s(t) = (9t3 , 7t2 ) at time t = 6…

Q: dx If x2 - 2x - 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: Given that lim f(x) = 0 Xa lim g(x) = 0 Xa lim h(x) = 1 x-a lim p(x) = co lim g(x) = ∞, evaluate if…

A: We need to find limit.

Q: Sketch and determine the opening, vertex and focus of the parabola with an equation of y2 - 8x + 16…

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Q: Sketch and determine the center, foci and vertices of the ellipse with an equation of x? (y-4)? = 1.…

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Q: 4 Using Trigonometric Substitution x2 +4x - 5 dx = | f(e)de find the new limits of integration. X+2…

A: By using Trignometric Substitution fin the limits∫14x2+4x-5x+2dx=∫abf(θ)dθ

Q: 3) consider the regionnin the second quadrant betueer the circles x?+yZ=4andx2+y2=25, and above the…

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Q: Use the Laplace transform to solve the initial value problem. y''+6y'+34y=136, y(0)=3, y'(0)=0…

A: Solution is given below:

Q: Which of the following is Inx – 6x + 18| + arctan(- (x – 3)) +C equal to? 2 – 6x + 18 x - 3 V 2 In…

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Q: Given the area  in the first quadrant by x^2 = 8y, the line x = 4 and the x axis. What is the volume…

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Q: f (x) = x1.5 + 2x. We have Find the tangent line L(x) for f(x) near x = 4 and use the tangent line…

A: Consider a function f that is differentiable at a pointx=a.Recall that the tangent line to the graph…

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A: We have to find the following conditions according to the given graph of the function

Q: 6. A bax with a square base is to have an open top. If the lateral surface of the bax is 100 cm",…

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Q: Use differentials to approximate the value of (3.01)2 + 2(0.99) – 3 in four decimal places.

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Q: Evaluate the integral 3 2x cos(xy)dydx 2

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = t’i + t°j 70 t4 K(t) (4 + 49 t10)ž

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Q: lim - Va +1

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Q: Consider the following function and closed interval. f(x) = x3 - 4x2 – 16x + 5, [-4, 4] Is f…

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Q: Compute the derivative of the given function. f (x) = 2 ln x – vT

A: Given fx=2lnx-x To find the derivative:

Q: 1 1) [ (tan³ 0 + tan³ 0) e-tan º d0== 2 (-1)" n! (In x)" dx= (m + 1)"+1 ·

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Using integration by parts, which of the following options is true x arcsec x dx ? xdx A. * Arcsec x…

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Q: Integral 1.

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Q: 2x4 +3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)? - B + E |dx x+1'…

A: we can reduce into partial fraction

Q: dx Vx²+2x+5

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Q: 27. 12f(r) – g(x)] dx = 28. Ư(x) – g(3)]dx =, 29. (4g(x) – 3f(x)] dx = 30. f) + 39(x)] dx =

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Q: I = 10+ 2s I - 1 y +3 12 - z Consider the lines defined by the equations ( : and l2: 9. y = 5s z =…

A: We have to find intersection Point of given line and equation of plane which contain both line.

Q: Compute the derivative of the given function. log3 x f (x) = %3D cot x - 2x2

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Q: give the equivalent cartesian coordinates of ρ = π

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 22 - 12x dx x?(3x² – 10x – 8) partial fraction is to be employed. What is the most appropriate form…

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Q: 2) Calculate lim ( In(3x + 1) – In(2x + 1)). -

A: Since you have asked multiple questions, we will solve the first question i.e., Question-(2) for…

Q: A doll-manufacturing company wishes to create a display box with a square base and open front side.…

A: Let's find.

Q: A stone is dropped from the upper observation deck of a tower, 800 m above the ground. (Assume g =…

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Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Svain2x dx =uv- fvdu - Svau. x/x In 2x- Vx dx v- Svau- Using Integration By Parts, Find uv- Jv du O…

A: Find your answer below

Q: Given the function f(x) =2+3x - x³. Determine the intervals where f is increasing or decreasing,…

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Q: (xcosx + sinx) dx + -sinx + 6 )dy y = 0;x=0;y=1 |

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Q: (x² -2x9 dy Solve The firest orler oDe

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Q: (1 – x²)dx eTextbook and Media 2) V You answered correctly! Move on to the next part to add to…

A: According to guidelines we solve only first question.

Q: Find the limit or explain why the limit does not exist: x2 + 3x lim sin x Note: x is measured in…

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Q: Q2: Determined the component of the vectors at each point…

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Q: 7 -4 Consider the surface x'z* + sin(y zª) + 9 = 0. Use implicit differentiation to find the…

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Q: Evaluate the definite integral. esin (a) cos(x) d x

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Q: Using trigonometric substitution, what is dx ? A sec + C 2x2 Vx² – 9 +C sec-1 6x2 none of the…

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