Perform the long division (x5 + 2) / (x2 - 1)and write the partial fraction decomposition of the remainder term.

Q: What is the standard linear approximation?

A: A linear approximation is an approximation of a general function using a linear function. They are w...

Q: Perhaps the simplest change of variables is theshift or translation given by u = x + c, where c is a...

A: (a) Prove:  ∫abf(x+c) dx=∫a+cb+cf(u)du Proof: Consider Left Hand side: ∫abf(x+c) dx. Let x+c=u      ...

Q: Definition of a Limit

A: Let  f ( x )  be a function defined on an interval that contains  x = a , except possibly at  x = a ...

Q: Write the equation of the line that passes through (-1,3) and (2,6)

A:  

Q: Calculus Question

A:

Q: Let sin t = a, cos t = b, and tan t = c.Write the expression -cos t + 7 cos(t + 1000π) + tan t + tan...

A: Given that, sin t = a, cos t = b, and tan t = c And, the expression is:  -cos t + 7 cos(t + 1000π) +...

Q: An arena held a concert and sold tickets for two types of seats: lawn seats and regular seats. Lawn ...

A:

Q: Find the length of the curve with the given vector equation. r(t) = cos ti+ sin tj+ 3t k; 0sts3

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Q: Solve the following equations for the real numbers, x and y. (3 + 4i)2 - 2(x - iy) = x + iy

A: Solve the following equations for the real numbers, x and y. (3 + 4i)2 - 2(x - iy) = x + iy

Q: Graph the curve and visually estimate its length.Then use your calculator to find the length correct...

A: Given: y=x2+x3, 1≤x≤2 To Find: i. Graph the curve and visually estimate it's length.ii. Find the len...

Q: The problem involves trigonometric equation quadratic in form.Solve the equation 2 sin2 x = sin x + ...

A: 2sin2x=sinx+3

Q: Solve quadratic equation. 1/x +1/(x + 3 )=1/4

A: 1x+1x+3=14

Q: S (x2Vx3 – 3 + 70) dx

A: Given,         ∫x2x3-3+70dx

Q: Carry out the following steps.a. Use implicit differentiation to finddy/dx.b. Find the slope of the ...

A:    

Q: Continuity of compositions Find functions ƒ and g such that each function is continuous at 0 but ƒ ∘...

A: Find functions f(x) and g(x) which are continuous at x=0 but f(g(x)) is discontinuous at the same. C...

Q: Evaluate the integrals ∫7 cos7 t dt

A: We have to evaluate the integral: ∫7 cos 7t dt Solving by substitution method, Assuming, z=7t Differ...

Q: Use sin2 u + cos2 u = 1 to prove that 1 + cot2 u = csc2 u .

A: Since the equation is  1 + cot²u = csc²u      

Q: Find the derivative of the function.

A: st=1+tt+34

Q: Verify the identity cot(-x) sin x = -cos x.

A: Given: cot-xsinx=-cosx

Q: A line’s slope is 7/9. The line passes through the point (−27,−17). Find an equation for this line i...

A:

Q: A ship sights a lighthouse directly to the south. A second ship, 9 miles east of the first ship, als...

A: Make a sketch using the available information. In the figure, d represents the distance of the firs...

Q: Determine the amplitude, period, and phase shift of the function y = sin(2x - π). Then graph one per...

A: We know that for a function: y=a sin [b (x + c)] + d Amplitude: a Period: 2pi/b Phase shift: c

Q: solve the given difference equation in terms of the initial value y0. Describe the behavior of the s...

A: Given differential equation is, yn+1=-0.9yn

Q: d'y Find implicity in terms of x and y dx? x² +y² = 4

A:  

Q: If a cylindrical tank holds 100,000 gallons of water, whichcan be drained from the bottom of the tan...

A: Given function - V(t) = 1000001-t602             ...............(1)where,V(t) = Volume of water in t...

Q: suppose that f(m) = m2+18m+72. Solve f(m)=0

A: Given : fm = m2+18m+72

Q: Find the limit (if it exists). If it does not exist, explain why.

A: limx→4-x-2x-4

Q: Express the function in the form fo g. (Use non-identity functions for f and g.) G(x) 1 + X {f(x), g...

A: Given,G(x)=x1+x3

Q: Evaluate the following Triple integrals over the regions defined in the second column, if available.

A: Let the given integral be I -I = ∫12∫02∫-112+z2-xydzdxdyIntegrating first with respect to z -I = ∫12...

Q: Solve and graph the solution set on a number line: 3 l2x - 1l ≥21.

A: 32x-1≥21 On simplification, we get ⇒32x-13≥213    Dividing by 3 on both sides⇒2x-1≥7⇒2x-1≤-7  or  2x...

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.