Find the domain of r, and determine the interval(s) on which the function is continuous. r(t) = tan ti + j + tk

Q: Calculus Question

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Q: Find the area of the region enclosed by the curves defined by  y=x2-2x-2 and y-x+8

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Q: Find the sum of the given vectors. а - (4, 0, 1), ь - (0, 5, 0) a + b Illustrate geometrically. a +b...

A: Given  The vectors  are  a =(4 ,0 ,1)  and  b= ( 0 , 5 , 0)   

Q: Find the interval of convergence of the series Σ (x-8)n/(n6+2) from n=0 to infinity

A: Given series is We will use Ratio test to find interval of convergence of the series. By Ratio tes...

Q: Curve sketching Use the graphing techniques of  graph the following functions on their domains. Iden...

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Q: Evaluate the geometric series or state that it diverges.

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Q: In a circle of radius 8 miles, the length of the arc that subtends a central angle of 1 radians is m...

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Q: Solve the homogeneous equations. First put theequation in the form of a homogeneous equation. (x + y...

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Q: give equations of parabolas. Find each parabola’sfocus and directrix. Then sketch the parabola. Incl...

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Q: What is a reduction formula?

A: Reduction formulas: Reduction formulas are used to solve complex integration such as  Hyperbolic tr...

Q: In each of Problems 5 through 11, find the general solution of the given differential equation. 5.y″...

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Q: State the name of the property. 3 + 17 = 17 + 3

A: This equation is similar to A+B=B+A This is a commutative property.   

Q: Perform the indicated operations and write the result in standard form: √-27 + √-48

A: A complex number is represented as the sum of a real number and an imaginary number.  And the standa...

Q: Find the values of cot-1 2

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Q: Find the value of x at which the absolute maximum occurs (if it exists) for the function f(x) = -x2 ...

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Q: Find the area of the sector of a circle with radius 6 miles formed by a central angle of 265" square...

A: Given,    Radius of a circle is 6 miles and the central angle is 265o.   To find:   Area of the sect...

Q: Complete graphs of polynomial functions whose zeros are integers are shown. a. Find the zeros and st...

A: Given, The graph is given, with zeroes are integers

Q: 8x²e2° dx .3 (3) Evaluate

A: To evaluate:

Q: Use a calculator or program to compute the first 10 iterations of Newton's method for the given func...

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Q: Suppose you are solving equations in the interval [0, 2π). Without actually solving equations, what ...

A: We have given the two function of sin; sin x = 1/2 and sin 2x = 1/2

Q: A truck with 22-in.-diameter wheels is traveling at 50 mi/h. Find the angular speed of the wheels in...

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Q: Differentiate. y = In Sin x  - 1/2Sin2 x

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Q: Laplace transforms A powerful tool in solving problems in engineering and physics is the Laplace tra...

A: We have given the function; f(t)= cos at

Q: Trigonometric substitutions Evaluate the following integrals using trigonometric substitution.

A: Now put,

Q: Consider a continuous random variable X with probability density function given by f(x) = { 0" Į kx ...

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Q: Use a sum or difference formula to find the exact value of the expression sin 195°

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Q: Consider the following definite integrals.a. Write the left and right Riemann sums in sigma notation...

A: Consider the integral equation: Left  Riemann Sum is given by:

Q: Simplify √27 ?

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Q: Consider making monthly deposits of P = $1050, dollars in a savings account at an annual interest ra...

A: Given that,  Deposited amount, P=$1050 , r = 0.9% = 0.009 Find  balance A in the account after 35 ye...

Q: Suppose an object moves along a line with velocity (in ft/s) v(t) = 6 – 2t, for 0 <t< 5, where t is ...

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Q: Find the limits

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Q: Solve the rational inequality: (x + 4)(x - 1)/(x + 2) ≤ 0and graph the solution set on a real number...

A: Given, We will set the numerator and denominator equal to 0 and find x.  So, x=-4, 1 , -2    

Q: Evaluate the integral using integration by parts with theindicated choices of u and dv .   ∫x2 ln x ...

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Q: Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine...

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Q: Express the sequence {an}∞n = 1 as an equivalentsequence of the form {bn}∞n = 3. {n2 + 6n - 9}∞n = 1

A: Given

Q: Find the average value of ƒ(x, y) = x cos xy over the rectangle R: 0≤ x ≤ π, 0 ≤ y ≤ 1.

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Q: Evaluate the function at the given values of the independent variable and simplify :    f(x) = 3x + ...

A:  f(x) = 3x + 7    .......................(1)   a. f(4) put x = 4 into eqn(1) f(4) = 3*4 + 7        =...

Q: Let f(x) = x2 - x - 4 and g(x) = 2x - 6.Find (f ∘ g)(x).

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Q: Refer to image

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Q: The monthly sales S (in thousands of units) of a seasonal product are modeled by S = 58.3 + 32.5 cos...

A: We use a graphing utility to graph the given function.     

Q: Find the largest and smallest values that the function ƒ(x, y) = xy takes on the ellipse x2/8 + y2/2...

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Q: Which of the functions satisfy the hypotheses of theMean Value Theorem on the given interval, and wh...

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Q: Use the Intermediate Value Theorem to show that f (x) = x5 + x3 − 5x + 2 has a root (that is, takes ...

A: Given equation is  

Q: Specify the x- and y-intercepts, specify the vertical and horizontal asymptotes (if any), and then s...

A: Given, A function          

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.