A. Evaluate the limit of a function using the concept of Special Limits. 1. lim t→0 t t2-3t+5 + t2-1 sin?t 2. lim sint t-0 8. Evaluate the limit of a function using the concept of indeterminate forms. 6х2-7х-3 1. lim 2х-3 V2x- V6-x 2. lim X-2 4-x2

Q: Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3rVx+ 2 10 4. -…

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Q: B. Evaluate the following 1 dx 2. 2 tan(x)dx 3.

A: We have to slove above question

Q: Evaluate: Je* cos (7e*)cos (4e*) dx ® -co (3*) -cos (11e') + C -(-*)* sin (3e“) –sin (11e*) +c A 22…

A: The given integral,       ∫excos7excos4exdx

Q: ト+ se=Atzメ

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Q: Q1) Evaluate the following integral using Partial Fractions Method: x3 + x? dx х2 + х — 2 y I|

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Q: Question 5 For what value of a is the function t-1, - 10<t<3 f (x) = t²+ 10t, 3<t<10 continuous? O…

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Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 15у — 12z — 2 %3D 0 (a)…

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Q: / sin*0 d0, factor sin*0 as (sin²o)² sin® and let sin²0 = -(1– cos20). To evaluate A True False

A: Given problem:-

Q: Q2) Convert the polar functionr tan20 to cartesian.

A: Here we have to convert the polar function r=tan(2θ) to Cartesian.

Q: What is 2x4

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Q: Find the volume of the solid that results when the region enclosed by y = Vx, y = 0, and x = 81 is…

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Q: Let f be the function defined by ƒ (x) = cos( (/T). (a) Approximate the definite integral| f(x) dx…

A: We have to find the definite integral by using midpoint riemann sum and trapezoidal rule

Q: Q4/ solve the equation by Newton -Raphson Method: F(x) = x* - 5x + 65 , start at x =2, accuracy…

A: Given

Q: inside polar functionr = 2 and outside p in third auartor

A: We have to find the area according to the given information

Q: 6. Use Laplace transforms to solve the initial value problems: (b) x" – x' – 2x = 0; x(0) = 0, x'(0)…

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Q: k=1 2K (c) Use the ratio test for absolute convergence to determine whether the series converges or…

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Q: From Rogawski ET 2e section 10.3, exercise 5. Use the Integral Test to determine whether the…

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Q: Q3) Find the Area bounded by the curves x and x = 2y – y².

A: Topic = Area Area bounded by curves is 13.

Q: Twins graduate from college together and start their careers. Twin 1 invests $1500 at the end of…

A: The question is based on the concept of Financial Management.

Q: Find (a) if fx) = /x-a+1.

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: Let's find.

Q: Differentiate the following functions. Show your complete solutions and emphasize your final answer.…

A: 1) f(x)=25x    Differentiate with respect to x   f'(x)=252) f(x)=-4x5+2    Differentiate with…

Q: 2.Find the indicated limit or state that is does not exist x* – y* C. lim (x,y)→(0,0) x² +y ху d.…

A: Solving

Q: Find the area of the triangle with vertices P(1,2, –5), Q(0,0,0) and R(2, 4, 1). NOTE: Enter the…

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Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 Y 4 9 10 10 9 3 n 00

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Q: Sx³e** dx

A: To evaluate: ∫x3e4x dx

Q: Question Using Rolle's theorem for the following function, find all values c in the given interval…

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Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: Question 1 Which of the following is the Taylor series expansion of the function 'f (x) =e¬x² with…

A: Given problem:-

Q: (b) Repeat part (a) using 3 subintervals and the velocity at the midpoint of each subinterval. mi

A: answer is in next step

Q: Evaluate r(g(t)) using the Chain Rule: r(t) = (e', e", 4), g(t) = 2t + 5 %3D r(g(t)) = ( %3D

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Q: 02) Solve the D.E dy - (2x/1-y2)dx 0

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Q: Solve the D.E dy – (2x/1- y2)dx = 0

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Q: Evaluate f s 2°ds О а. 2"(sin2 - 1) (In2)2 O b. 2(sln2 - 1) (In2)2 O C. 2* In2 O d. 25 In2

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Q: Find the volume trapped below the cone z = Vx² + y² = r over the semicircular disk: 2.0 y r dr do…

A: We need to find volume.

Q: Determine the equation of the tangent to the graph of y = [2~/x - x][1+ /x - x ] at the point (1,…

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Q: 3. Determine the following a A negative angle in radian measure coterminal to Show calculation steps…

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Q: -2e dx

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Q: find the rational number represented by the repeating decimal. 0.451141414

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Q: From Rogawski ET 2e section 10.3, exercise 3. Use the Integral Test to determine whether the…

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Q: 5. In antidifferentiation, the formula J x" dx : + Cis valid if? (n+1) C. ne {0,1,2} A. nER 6. In…

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Q: Q2) Solve the D.E xy(x? + 1)dy - (y? + 1)dx = 0 %3D

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Q: If Ax) = a(x-h)* +k, where a, h, and k are constants, find f"(). 2ax O 2(x-h) O ax+h+k 2a

A: The given function is f(x) =a(x-h)2+k,   where a, h, k are constant. We have to find f''(x) f''(x)…

Q: 12x 3 3 15 12 x4

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

A: Let's find.

Q: Question For the function given below, which statements concerning Rolle's theorem are true? —3х - 1…

A: This question is related to Rolle's theorem, we will solve it using given information.

Q: Find each of the following indefinite integrals.  c. Z (r+2)^2/r^3 dr

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Q: y = Vx* X

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Q: Find the smallest number n of terms needed to obtain an approximation of the series 27ke-0.254² k=1…

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Q: Find a polar equation for the curve represented by the given Cartesian equation. 9. a? + y? = 25

A: Given equation x2 + y2 = 25 To be found : Polar form.of given equation.