Find the smallest value of k e N for which the area under the graph of f(x) = x* + x between x = 0 and x = 1 is less than 0 31 k =

Q: 1. Find the limit of the following: ** - 11х* +37х* +6х' - 297х +621x - 405 x* - 11x* +47х* -114х* +...

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Q: QUESTION 1 d²y Find dx² for each of the following equations. a) y = 3x² + cos(3x) b) y = e** + (x + ...

A: Given that: (a)y=3x2+cos(3x)(b)y=e4x+(x+1)4

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Q: 1. fcos*ysin ydy

A:  In this integral,  you can see cosy2 has exponent 4 and siny2 has exponent 1. To solve this integra...

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A: We can use an augmented matrix to solve the given non-homogeneous system of equations.

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Q: 17. Find the volume of the solid generated by revolving about the x-axis the region bounded by the u...

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Q: Find the general solution of 4y'- 23y" - 33у" -17у — Зу 3D 0

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Q: dx Evaluate the given function : Vä(1+væ)

A: Here we have to evaluate the given integral.

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Q: To improve her handwriting, Hope practices writing the numbers from 1 to 200. How many times will sh...

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Q: 1+1=?

A: Given that we need to find the value of the following expression.

Q: 8. Find the exact value of each expression. 3V34 tan cos 34

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Q: Write down the first five terms of the following recursively defined sequence. a1 = -5; an+1= -2a, +...

A: Given sequence is  an+1=-2an+5with a1=-5To find the first five terms:  

Q: Solve in detailed solution A. Í (4x³+x) v4x²+1dx B. (x+2) Vx+3dx

A: Let I=∫(4x3+x)4x2+1dxI=∫x(4x2+1)4x2+1dxI=∫x(4x2+1)(4x2+1)1/2dx I=∫x(4x2+1)32dx Put (4x2+1)=udifferen...

Q: ii. 0.9,0.99,0.999, 0.9999,..

A: This can be written as  9/10, 99/100, 999/1000, 9999/10000..... (10-1)/10, (100-1)/100, (1000-1)/100...

Q: Solve the differential equation (y¯+ y)dx - (y¯+ 2xy + x) dy = 0. If y = 1 when x = 3, determine x w...

A: Topic:- differential equations

Q: y = Arc tan Vx

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Q: (5 + 4) + 6 = 5+ (4 + 6) illustrates the property of addition.

A: This question is related to algebra.

Q: Find the sum of the infinite series, if it exists. -16 -64 32 8, , 5, 27· 3 Enter the sum as a fract...

A: The given infinite series,8, -163, 329, -6427,.......

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A: To evaluate:∫xx2-1x2+1dx

Q: / (3cosh m 2 cosh m sinh mdm +e°

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Q: 2. Evaluate the following functions using the given relations. f(2) = -1 ; Relation: f(n+1) = 5 - [f...

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Q: Find the derivative of f (x) = (4x + 1)(5x² + x/x ). Upload your work in the next question. The deri...

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Q: Prove the following indentity. - 1 attachment - sece sine = cot0 sino cos0

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Q: Find the value of the line integral given below. (Give your answer correct to 2 decimal places. Hint...

A: Given: F(x,y)=yexy i+xexy j

Q: Find the parametric equations for the tangent line to the curve x=t^2−1,y=t^4+1,z=t^4 at the point (...

A: Given: x=t2-1, y=t4+1, z=t4 Point 8, 82, 81, is for t=3 as you can see substituting it in the three ...

Q: the population of a colony of hamsters grows exponentialy. the colony begins with 10 hamsters five y...

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Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the ...

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Q: Evaluate the definite integral 2 (5e +8x)dr using Part 1 of the Fundamental Theorem of Calculus. Ent...

A: Given problem:-

Q: d?y dy + 5 14y dx2 dx Determine the Characteristic Equation for the given Differential Equation.

A: For solving such differential equation we put y=erx, where r is any constant.Since , d(eax)dx= a eax...

Q: Prove: 0 =- 1 Proof 1: sin x tan xdx = [ cos x 1 u = cos x dv = sin xdx sec x du = sec x tan xdx v=-...

A: Solution is given below:

Q: 1. Prove that lim (10z – 7) = 3 using epsilon-delta definition of a limit.

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Q: Write the trigonometric expression as an algebraic expression in u. cot ( cos 'u) cot (cos 'u) = (Ty...

A: Inverse function

Q: |The vector projection of v = 4î + 4j + 4k onto W = 5î - 4ĵ + 3k is aî + bî +cê: where the exact num...

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...

A: Given that: ∫x2+1(x-3)(x-2)2dx

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Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 ...

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Q: a) Queen Beyoncé's yacht will be leaving from Port Destiny and traveling on a straight line to an is...

A: Each part of the problem is solved below in detail.

Q: Determine whether the given sequence converges, and, if it does, find the limit. i. An sin () %3D

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the...

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Q: The average change of a function f over an interval [¤1, x2] is f(x2)-f(x1) First find the average r...

A: We can find the instantaneous rate of change as below

Q: valuate the integral below along the path C. (Give your answer correct to 2 decimal places.) | (2r –...

A: The detailed solution is given below Thank you  The final answer is -101.48

Q: (vz-i, »). a Let 7(t) = (/2-i -1+e' In(t + 1) (i) The domain of 7 is [a] (input a number from below)...

A: The domain of a vector function is the set of all t for which all the components of vector are defin...

Q: . 2yda + (x – x³y³) dy = 0

A: here we have to check whether the differential equation is exact or non exact.

Q: 5 Suppose S f (x) dr = -8 and S g(x) dx=9. %3D -3 -3 | Evaluate S (2 f (x) + 4 g (x)) dr. -3 Remembe...

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Q: Q2: z = cos3xsin4y+2x²y az az azz a²z a2z Find : дх' ду' дх ду 'дхду

A: Given  z=cos3x sin4y+2x2y Differentiating partially with respect to x and y , we get ∂z∂x=(-3sin 3x)...

Q: a videoke machine can be rented for php 1000 for three days,but for fourth day onwards,an additional...

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