Evaluate each of the following limits. Тапх-x 1) lim х-0 х-Sinх

Q: If log, (5x + 6) = 5, then x = You may enter the exact value or round to 4 decimal places. > Next…

A: We will solve for x.

Q: For y = arccot(7 e*) dy da

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Q: (2xy + 3y²) dx – (2xy + x²) dy = 0 .. [VARIABLE SEPARABLE/HOMOGENEOUS |

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Q: 7 If the change of variables u = x-1 is used to evaluate the definite integral f(x) dx, what are the…

A: This question can be solved using the concept of change of limits in definite integrals.

Q: Evaluate the limit using L'Hospital's rule 1 - 10x lim 10xe -

A: Given query is to find the value of the limit.

Q: A particle is moving with acceleration a(t) = 36t + 2. its position at time t = 0 is s(0) = 2 and…

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Q: f (x) +f (1 – 4 ) = x

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Q: dy Differentiate implicitly to find xp ex*y = 7x+ 3y +3 Evaluate the derivative of the each side of…

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Q: Write the first five terms of the arithmetic sequence. ad - 1 0.2 2. 10 14 21 3333 0.214 7 10 3333-3

A: This question can be solved using the concept of general term of arithmetic sequence.

Q: x²-4 dx 2. XV xvx²-9

A: ∫1x2+a2 dx =1a tan-1xa+C.

Q: de

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Q: olve the triangle. Round your answer to the nearest tenth. A 95° 20 40° C B mLB = 45°, a = 28, b =…

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Q: Find the area of the region enclosed by the graphs of x + (y – 1)² = 1 and 2x = -y?.

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Q: 4 8. + 6. 16 Consider the following geometric series: 2+ + .... Identify a and r, find a formula for…

A: The given series is  2+4/3 +8/9 +16/27+...

Q: 1 ): The vectors 2 and form a basis the vector space R'. Select one: O True O False

A: Here we state whether it is true or false.

Q: Using your knowledge of calculus find (and also show that it is) the vertex of a general parabola…

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Q: 1. Algebra: Compile 1 application problem for introduction to algebra with solutions and correct…

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Q: Evaluate f x(x- 1) dx | c. (x + 1) -x + 1) +C D.x – 1) -- 1) +c x(3 35 1)z (x- | | 35 35 35 |

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Q: Exercise 1. Find the following limits 2 3x + tan 2x 2x + x tan 2x sin 1) lim 2) lim 5x +x tan 2x 3)…

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Q: sin(x) 1- sin? (x) 3. Evaluate the integral O 2ln|1 - sin2(x)| + C O -csc(x) + C sec(x) + C O None…

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Q: An airplane flying at an elevation of 3,500 ft., directly above a straight highway. Two motorists…

A: Let d be the distance between the two airplanes

Q: 1 What is the instantaneous rate of change of Y= at x = 2? - o-1 4 O none of these -1 -1

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Q: A) lim x→3−    f(x)= B) lim  x→3+    f(x)= C) f(3)= D) Determine whether the function f is…

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Q: sin x 2. Find the derivative of y = 3+2cos x

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

A: We have to find the distance

Q: Find the cofactor matrix of the following matrix 1 0 1 A = 4 -2 5 1

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Q: Complete the following steps for the given function, interval, and value of n. a. Sketch the graph…

A: To find out the riemann left sum and right sum and also sketch the graph.

Q: Q: The differential equation whose auxiliary equations roots are 2,2,1 is (a)Ae* + Be2x* + Ce2x (d)…

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Q: Suppose the position of an object moving horizontally after t seconds is given by the following…

A: Given equation is quadratic so accordingly draw the graph and then solve .

Q: 3u' = - 3x + 5y Solve the system of differential equations x' 2х + Оy l y' = 3x + 5y - x(0) = 3,…

A: We solve here given differential equations and find the value X(t) and Y(t).     Here i attached the…

Q: The graph of a function is given. Use the graph to find the value does not exist. ta fx) b. f(1) -21

A: solution:-(a)According to the given graph of function f(x)limx→1 f(x)=-3becauseleft hand limit…

Q: Problem 5 Solve (y')? + 2 y' – 3

A: We need to solve D.E.

Q: Find the domain and range of y = log,(7 + 5x). The domain is: The range is : > Next Question

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Q: Find the equation of the tangent line at the given point on the following curve. x* +y = 20. (2, –…

A: The given curve,    x2+y2=20, 2,-4

Q: C) 8 +C

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Q: csc2 3x Evaluate J cot³ 3x csc² 3x dx ● 금cot-23z +c O cot 23xcsc3x + c O 6cot 3xcsc3x + c ○ 글cot?…

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Q: Question 3 [ a} J: Determine whether the following series (-1)"5"-1n Σ 42n+1 n=1

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Q: 4. If the characteristic equation of the differential equation y"+2y'-3y =0 is m² + 2m –3 =0, then…

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Q: Use Lagrange Multipliers to solve the following: Maximize f(r, y, z) = 4x + 2y + z subject to z2 + y…

A: We have to maximize f(x,y,z)

Q: 3. Which of the following is the same as [(z-2)(3z+5)dz? A) [(z-2)dz + [(3z+5)dz B) [ ziz-2fdz+3[zdz…

A: ∫(z-2)(3z+5)dz ∫ (3z2 +5z -6z -10)dz ∫ 3z2dz  - ∫zdz -∫10dz option C is same as given so answer C is…

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: Question 1 ( (a) Use the Second Derivative Test to find the local extreme values of the function…

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Q: If f(æ) = 8 sin-(*), then f (2) =

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Q: b. In the interval (0,5), f is not differentiable at x = (Use a comma to separate answers as…

A: Function is not continuous at those point where the graph of the function has missing points in…

Q: Compute the partial derivative: f(x, y) = sin (a- 6y) f,(0, T) =

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Q: s required to repay a loan that matured to $4,550 on August 14, 2015. ne realized that he could…

A: Topic:- simple interest

Q: 10) 4xy dx - (6x² +y) dy so

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Q: Given the function y = x3 - 5x2 - 8x + 3. Determine the following: a. maximum point b. minimum point…

A: The given function,  y=x3-5x2-8x+3

Q: Find an equation of the plane. The plane that passes through the point (−2, 3, 2) and contains the…

A: This question can be solved using the concept of planes in three dimensional geometry.

Q: Evaluate the following expressions. sin (tan-(1)) cos (tan-(0))

A: We need to evaluate given functions.