x - 5, x21 (b) A function ƒ is defined by f(x)=. 1 x<1 Show that f is differentiable at x = 1. Hence, state whether is continuous at x =1.

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

A: The given series is ∑k=0∞78k+2. We have to check whether the series converges. To check converges we...

Q: Find the radius of convergence of the power series. (If you need to use co or -m, enter INFINITY or ...

A: Consider the power  series            ∑ an (x-a)n then Series will convergent if |x-a|&lt;R , where ...

Q: (-1)"n! 3. (a) Test the series for absolute convergence. n" n=1 2 4 2n-1 (b) Prove that the series 1...

A:

Q: x - 36 lim X6 x+6 (a) Vx +11-4 (b) lim- x-5 (c) lim- X-2 2-x (d) x' +6x +9 lim x+3

A: a) limx→ -6 x2-36x+6 =limx→ -6 (x-6)(x+6)x+6                     ( using factorisation              ...

Q: a. Show by means of slope that the four points (0,0), (-2,1), (3,4), and (5,3) are vertices of a par...

A: This is a problem related to geometry. For parallelogram opposite sides are parallel to each other. ...

Q: 2.

A:

Q: By using chain rule Find dy/dx iff- u=-1, x=-1

A:

Q: Question 7 Consider the integral dx . Using u-substitution, what is the appropriate u and du? -2x 2e...

A:

Q: / 5x? tun(3x) dx. If u= 3x³, then the resulting integral is Jf(u) du. Find f Given: 5/2 A 18 B none ...

A: This question can be solved using the concept of substitution as used in integration.

Q: Determine whether the given series is absolutely convergent, conditionally convergent or divergent. ...

A:

Q: Find the Maclaurin polynomials of orders n = 0,1, 2, 3, and 4 and then find the nth Maclaurin polyno...

A:

Q: Question 8 12x +1 dx. (2x- 1) (3x+2) Evaluate: 1 A (2x- 1) (3x+2)? %3D B) In (2x- 1)? (3x+2)| + C (2...

A:

Q: In general, a partial fractions integral with a repeated irreducible quadratic factor will result in...

A:

Q: an+1 to determine if the sequence {ne" } is strictly increasing or strictly decreasing. an Use the r...

A:

Q: x2 dx. Which of the following options is correct? 00 Consider 9+x6 00 Arcsin 9. + lim - Arcsin 3 A l...

A:

Q: Differentiate the function by using the definition of derivatives. f(x + h) – f(x) f'(x) = lim h f(x...

A:

Q: Use the binomial series to find the Maclaurin series for the function. f(x) =  1 (1 + x)3

A:

Q: Find the nth Maclaurin polynomial for the function. 2x – 5 - f(x) n = 4 %3D X + 1 P(x) = %3D

A: According to question,Given Function,fx = 2x-5x+1n = 4

Q: 22 Use a triple integral to find the volume of the given solid. The solid enclosed by the evlinder x...

A: According to question,Given Cylinder and planes,x2 + z2 = 4y = -1y+z = 4

Q: Use any method to determine whether the series converges or diverges. (k!) Σ (6k)! O The series dive...

A:

Q: 8-2х (f) lim- нх* — х—12

A:

Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) = (1 + x)4 Σ f(x) n = ...

A: Explanation of the answer is as follows

Q: 6 du Consider dx. Transforming the integrand, the result will be where k is a constant. What is u an...

A:

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: We know that the Taylor series is given byf(x)=∑n=0∞fn(c)n!(x-c)nHere we need to find the Taylor ser...

Q: ,3x S- -dx be given. If 4=e*+2. then the resulting integral is Jf(u) du. compute f (3). e +2 Let

A:

Q: 8. What is de x2+1

A:

Q: Find the general term of the sequence, starting with n = 1, determine whether the sequence converges...

A: Given sequence is GP. and ntg term of gp is an =arn-1

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c= 5 (x- 5)4 12...

A:

Q: Given: / 5x2 tan(3x³) dx. Ifu=3x°, then the resulting integral is Jf(u) A B none of the choices 5 18...

A:

Q: Find the centroid along the y-axis of the plane area bounded by the equation y^2=4x, x=1 and the x-a...

A: Given curve is y2=4x ,x=1

Q: Solve the following ODE. y" + 2y" – y- 2y = 9 - 123 NOTE: Write arbitrary constants as c1, Cg, and c...

A:

Q: dx S (x² – 6x + 13)² 4.

A:

Q: 3. Suppose that z = f(x, y) is a differentiable function with respect to variables !! x and y and is...

A:

Q: cot (2x) Evaluate the integral - * xp- V cor (2x) - 15 csc (2x) (A) -Arcsec +C 4 (B -- In cot (2x) +...

A:

Q: Use the following results, if needed, to determine whether each series converges or diverges. uk con...

A: (a) To test the convergence of the series ∑k=2∞1kln k5-1k5, we will analyze the convergence of the s...

Q: • f(x) (x) , evalu:

A:

Q: f(x) = 3√3x^2 + x + 1  take note: fuction of x is cube root of 3x^2 + x + 1 (a.) the critical numb...

A: As per bartleby guidelines we only give first three suparts  question answer.

Q: Consider the following sequence: {an} = an+1 Use the ratio an - to show that the given sequence {a, ...

A:

Q: Do the following: (a) Construct the table of values; (b) graph the function; and (c) find the indica...

A: Since you have posted multiple questions in this question which are not interlinked so I have solved...

Q: Determine whether the series converges. k=1

A:

Q: dx The integral can be re-written as. VI- A lim (-2+ V1- m) m-- 00 B none of the choices lim (2-2 V1...

A: ∫-∞0 dx1-x  

Q: When you perform polynomial long division on the rational expression a²+3x+3 the numerator of the re...

A: The rational expression,    x2+3x+3x+1

Q: /1 + dt and g(y) f(x) dx, find If f(x) g"(T/6).

A: We have to find value of g"(π/6)

Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1 + x f(x) = 1 + x+ 4...

A:

Q: 5. Find the centroid of the solid formed by revolving the area between the curves: y? = x and y = 2 ...

A:

Q: Use Green's Theorem to calculate (422 – 3yx)dr + (3xy+ y² + 6)dy where C is the circumference (x – 1...

A:

Q: 8. What is de x2+1

A:

Q: 2. (a) Prove the following inequality n(n- 1) ,2, 120 (1+ 1)" 2 1+ nz + 2 for any n 2 1. (b) Show th...

A:

Q: (d) The function k(x)is defined as follow: 3 x+ 17 -- 4 k(x) = { 2, x =1 5|x-1| x² -1 x>1 Discuss th...

A:

Q: Consider the following sequence: 5" {an} = n=1 An+1 Use the ratio to show that the given sequence {a...

A: Given sequence an=5n2n2n=1+∞