27. 3* dx

Q: Find lim(x→−2)(x^2 − 4)/(x^2 − x − 6)

A: We first factor the numerator and the denominator  

Q: 4. The teardrop x = 2a cos t – a sin 2t, y = b sin t, 0 < t < 27 find area y 2a

A:

Q: (a) Consider the integral | sin(5x) dx. Which of the following expressions represents the integral a...

A: Consider the integral:   Hence, B is the correct option.

Q: Find the angles at which the curve y=x3−x intersects the x-axis.

A: The angle at which curve intersect the x axis is determined by the angle of slope of tangent to the ...

Q: Find the slope of the tangent line to f(x) = e^[3 (x^2) − 4x] at the point (0,1).

A:

Q: find the general solution to the given Euler equation. 1.x2y′′ + 6xy′ + 4y = 0 2. x2y′′ - xy′ + 2y =...

A: The given Euler's equations are 1. x2y''+ 6xy′ + 4y = 0 2. x2 y''- xy′ + 2y = 0 3. x 2 y′′ + 7xy′ + ...

Q: Find the limit, if it exists

A: To find the limit, if exists.  

Q: Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflec...

A: Given that, y = −2x4 + 3x2 The x-intercept of the function occur where y = 0. ⇒ −2x4 + 3x2 = 0 ⇒ (−2...

Q: It is important to distinguish between\[\sum_{n=1}^{\infty} n^{o} \quad \text { and } \quad \sum_{n=...

A: Given: The series and .

Q: Evaluate the integral.

A:

Q: Find an antiderivative of the function f(x)=e2x.

A:

Q: Where does the parametric line (2 + 2t, t, t)intersect the plane x + y – 3z = 4? A) (4, 1, 1) B)1 C)...

A: The parametric line is given as (2+2t,t,t). and equation of line is x+y-3z=4 From the parametric lin...

Q: The graph of the derivative f' of a continuous function f is show below.

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Find the first partial derivatives of the function. f(x, y) = x6 + x2y2 + y6 fx(x, y) =        ...

A:

Q: Calculus Question

A: Since, we can answer only one question. We’ll answer the first question, since exact one wasn’t spec...

Q: Find the equations of the tangent and normal lines to the graph of the natural logarithm function at...

A: Slope of the tangent line is the derivative of the given function at the given point. Now differenti...

Q: Verify the solution of the differential equation. (Enter your answers in terms of x and C only.) Sol...

A:

Q: Which of these vectors is perpendicular to (1, 2, 3) ?MARK ALL THAT APPLY PLEASE. A) (–1, –1, 1) B) ...

A:

Q: use a triple integral to find the volume of the solid bounded by the graphs of the equations . z = 8...

A: Given

Q: Write the equation of a circle osculating with the curve f(x)=arctanx at the point x0=1.

A: Given: f(x)=arctanx x0=1.

Q: Find the general solution of the first-order linear differential equation. xy' + y = x³3 + 1

A:

Q: 40. Find the circulation of the field F = yi + (x + 2y)j around each of the following closed paths. ...

A:

Q: Graph the functions in Exercises 23–26 in the ts-plane (t-axis horizontal, s-axis vertical). What is...

A:

Q: In Exercises 1–2, sketch the region bounded by the given lines and curves. Then express the region’s...

A: (1) Given Data The equation of the line is x+y=2   Substitute the values in expression x+y=2 at y=0,...

Q: Evaluate the integral. show that it is divergent.  integral 1/ ( 2x + 3 ) 2 dx

A:

Q: Find the acute angle between the planes x + y = 1 and y + z = 1.

A:

Q: On which interval(s) is the function h(t) = (−t^3) + 3(t^2) + 24t − 11 decreasing?

A:

Q: Find the limits. Are the functions continuous at the point being approached?

A:

Q: Write the sum using sigma notation: 2 + - 5+ = 12 +... + - 89 Σ Preview i=1

A:  

Q: Find two positive numbers that satisfy the given requirements. The product is 185 and the sum is a m...

A: Let x and y be the required positive numbers. Now given that the product is 185. That is, Now consi...

Q: Find the general indefinite integral. Thank you!

A:

Q: Find  product.  (4x + 5)(4x - 5)

A:

Q: Evaluate the trigonometric function. Round your answers to four decimal places cos(−3/7 )

A:

Q: Find the values of the function. g(x, y) = x2e2y (a)    g(−2, 0)       (b)    g   2,  ...

A:

Q: Use the limit process to find the area of the region bounded by the graph of the function and the x-...

A: The diagrammatic representation of the area is,

Q: Simplify the given expression.  ∛16x4

A: The given expression is

Q: Consider the length h of the perpendicular from point B to side b in the given triangle. Show that

A: The triangle ABC is  We have to prove   ,where  the length h of the perpendicular from point B to s...

Q: Let f ( x , y ) = 2 x − y + x2 + y4. Which (unit) direction vector u  MINIMIZES the directional deri...

A:

Q: Use the initial condition to find the particular solution of the differential equation. differential...

A:

Q: In Problems 31 through 42, verify that the given differential equation is exact; then solve it. 38. ...

A:

Q: Simplify complex rational expression. [(8 +1/x)/(4 -1/x)]

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Q: Find the derivative of f(x) = ln(2x^3 + x).

A:

Q: find integral 1 / x2  sqrt (x 2  +1) dx

A:

Q: Interval of convergence for a power series Use the ratio test to find the interval of convergence. D...

A:  

Q: Solve equation.   (x - 3)2 - 24 = 0

A:

Q: . Eliminate the parameter to find the standard form gedaa rectangular equation representing the grap...

A:

Q: Find the differential of the function y=sinx−xcosx.

A: Given, 

Q: find the value of ( ƒ ∘ g)' at the given value of x. ƒ(u) = 1 - 1/u, u = g(x) = 1/1 - x, x = -1

A:

Q: Subtract the infinite series of ln(1 – x) from In(1 + x) to get a power series for: + x Σ In %3D n=1...

A: Given:

Q: Find the exact value of the logarithm without using a calculator.

A: