Divide using long division. State the quotient, q(x), and the remainder, r(x). 4x³-5x²+6x+7 4x² + 3x +4 4x³-5x² +6x+7 2 2 4x + 3x +4 4x + 3x + 4 (Simplify your answers. Do not factor. Use integers or fractions for any numbers in the expressions.) = ... +

Q: 4. Consider the inequality | 2| < 3. As needed, reference back to the terminology of Exercise 3…

A: Given inequality  x−2&lt;3

Q: Evaluate the integral 1 d.x √4+x²

A: Here we have to use the u-substitution method.

Q: (11 points) Use the given graph of the function g to find the following limits: 1. lim g(x) = x-2-…

A: 1. limx→2-g(x)=2     2.limx→2+g(x)=-1

Q: 3. Let R be the region bounded by the graph of y = 1-² and by the positive coordinate axes. Using…

A: Volume of a solid form by cylindrical shell method is given by V=∫ab2πr(x)f(x)dx     where,   a≤x≤b

Q: Use the Product Rule or the Quotient Rule to find the derivative of the functic y = 7x5 sec(x) y' =…

A:

Q: Determine whether Rolle's Theorem can be applied to the function f(x) = (x+3)(x + 2)² on the closed…

A: Given that the function is         f(x) = (x+3)(x+2)2

Q: Evaluate the following limit: lim O O O - 7Inx lim x+19x³-9 - 7Inx lim x+19x³-9 lim x+19x³-9 - 7Inx…

A:

Q: For ε > 0, find ō > 0 necessary to prove lim (9x-30) = 15. X-5 O 6= € +5 6 = +40 6 = - € 30 = €

A: limx→5(9x-30)=15 Here 15 is limit of the function f(x) = 9x-30 when x tends to 5.

Q: Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify…

A:

Q: Use the rules of differentiation to find the derivative of the function. h(x) = 6√x +7√x h'(x) = 1…

A: We will use standard formula of differentiation to solve this.

Q: Find the point at which the line r(t) = (6, − 8, 1) + t(4, 7, − 2) intersects the yz plane. -

A: Here we have to find the point of intersection

Q: Suppose - 3x² +24x-53 ≤ f(x) ≤ 3x²-24x +43 for all x values near 4, except possibly at 4. Evaluate…

A:

Q: Write an equation of a line tangent to the graph 3x² = -3y² + 75 at the point (-4,-3).

A:

Q: Evaluate the indefinite integral. √x² + 1 da

A: Topic:- application of integration

Q: Consider the vector function r(t) = (t, t,t¹) Compute r' (t) = ( T(1) = ( r" (t) = ( r' (t) x r" (t)…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find the area of the shaded region. (2) A 1.39 B 1.69 D 1.25 1.50 1/4 <2, // ) X

A: I have appended the formula used in the solution part of the question

Q: Suppose that lim g(h) = L. h-0 a) Explain why lim g(ah) = L for any constant a 0. h→0 If we assume…

A:

Q: Consider the function f(x)=√x near x = -1. Find the linear approximation error when using the linear…

A:

Q: Find the average value and the value(s) of c guaranteed by the mear theorem for integrals if f(x) =…

A:

Q: A 13-foot long ladder is leaning against a house when the base begins to slip away from the house at…

A:

Q: sec(log3 m) dm mln 3

A: ∫seclog3mm ln3dm

Q: Evaluate √√cos cos x sin³ x dx.

A: ∫cosxsin3xdx

Q: Find all relative extrema of the function. See Examples 1, 2, and 3. (If an answer does not exist,…

A: The given function is hx=-x+73 we have to find its relative extremum. Use the derivative formulas,…

Q: Let f(x) = 3 cos x f'(x) = ƒ'( -5 ) 6 = 7 tan x

A:

Q: a Estimate the value of 2 3 x +4 width using Simpson's rule. Round the final result to five decimal…

A: The objective is to evaluate integral using simpsons rule.

Q: If z = (x + y)e*, x = 3t, find dz/dt using the chain rule. Assume the variables are restricted to…

A:

Q: Find the horizontal asymptote, if any, of the graph of the rational function. 16x 2 8x²² +3 f(x) =…

A:

Q: The second derivative of et is again et. So y = et solves d²y/dt² = y. A sec- ond order differential…

A: we need to find out the other solution of the differential equation.

Q: Evaluate J√si 3 sin x cos³x dx. + C

A:

Q: Find the nth Maclaurin polynomial for the function. 5X - 2 n = 4 X + 1 P4(x) = f(x) = Need Help?…

A:

Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A:

Q: (2) Evaluate evx -dx √x Watch the notation. Do not write x's limits with du. (5 points)

A: Please refer to the image below

Q: Differentiate the function. 7 x - 7x² +7 X X y' = y =

A:

Q: Find dy dx dx y=6( cscX+ cotx)( cscX- cơ -0

A: Topic:- calculus and derivatives

Q: Evaluate Answer: dt t² + t-30 S₁

A: ∫1t2+t-30dt

Q: roblem #1: Find the value of y' when x xy8 + ey/4 = e Problem #1: = 0 if Enter your answer…

A:

Q: Find the vertical asymptotes, if any, and the value of x corresponding to holes, if any, of the…

A:

Q: dy dt y = sin (tan (9t – 1)) Find dy dt

A:

Q: X for n ≥ 2. Prove the reduction formula I cos n-1 cos" x dx = ==cos". n n +¹=¹ / cos n asin x +…

A:

Q: Use transformations of the standard cubic function, f(x) = x³, to graph the function h(x) = 2x⁰. UL

A:

Q: Find the slope of the tangent line to the graph of the function at the specified point: b) y = 9…

A: We need to find slope.

Q: Section 4.1 Problems In Problems 1-8, find the derivative at the indicated point from the graph of y…

A: To find derivative of the given function.

Q: Make a table of values for the equation. y = 4 - |x| X -4 -2 0 2 4 у

A: The objective is to solve the above question.

Q: Determine whether the function given below has an inverse function. If it does, find the inverse…

A:

Q: 1 -1 2 a-c c+1 ¹] | = -1 2 7 1 0 c-3 0 1 0 {][ a 0 0 2a -2b 1 1 0 1

A: To create a system of equations to solve the variables.

Q: Let f(x, y) = 3x² - 8x + 3y + 2y² + 4xy. List the critical point: The critical point is a Select an…

A: Given function:- fx,y=3x2-8x+3y+2y2+4xy

Q: 6) In a town whose days after the disease has begun is given by the function population is 3500, a…

A: In a town whose population is 3500,a diagram creates an epidemic. The number N of people infected…

Q: (e) lim I→∞ /9x4+3x+2 4x³+1 (f) lim [2x] x- 8. Verify each limit using the definition of limit. (a)…

A:

Q: e product rule gives what derivative for ete-t? This function is constant. A = constant is 1. Then…

A: Topic:- function