Consider IVP: y' = y² + t², y (0) = 1. Using Euler's method with time step h find y (2) . 0.5.

Q: Calculate the Taylor polynomials T, and T3 centered at x = a for the function f(x) = 19 1n(x + 1), a...

A: Taylor series of function fx at a is defined as:       fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…=0+ddx...

Q: (a) Find (fo g)(x). (b) Find (g o f)(x). (a) (f o g)(x) =(Simplify your answer.) %3D

A: Topic:- function

Q: Evaluate the following integral by interpreting it in terms of areas: 3 dæ Value of integral =

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Q: Convert 7383 to a numeral in base 4. 7383 = D %3D 14

A: Topic:- algebra

Q: the figure given, determine force P that will give the body an acceleration of 2m/s given that the c...

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Q: 3 24- dx (3— 4x(х + 1)

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Q: For the following differential equations, determine a. order b. degree c. linearity(yes or no) d...

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Q: Consider the differential equation у" - у'- 30у 3D 0. Verify that the functions e-5x and e6x form a ...

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Q: If 11 < f(x) < 19, then | f(x)dæ <

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Q: Problem 2: (2y cos a + sin x) dæ sin a dy when a = , y = 1

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Q: Use the Simpson's Rule to approximate the given integral with n = 8. (Find S8.) Round your answers t...

A: Given,∫0211+x6dxHere n=8, therefore h=b-anh=2-08h=14 Now we create table  x 0 1/4 1/2 3/4 1 5/4 3...

Q: (x) dæ + f(x) dæ - f(x) dx 2. can be written as a single integral in the form | f(x) dæ Determine a ...

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Q: If the demand for q units of a product priced at $p per unit is described by the equation 200 V29 + ...

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Q: use newtons method for this calculus equation  show all steps f(x)=x3+2x+1

A: Given f(x) =x3+2x+1. We use Newtons Method to find a real approximate root of f(x). From Newtons Met...

Q: (-1)" 6. (0.999)" n=0 M:

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Q: 13) In Problems 13 through 20 given f(x) and g(x) are Continuous and Differentiable EVERYWHERE with ...

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Q: SA We have seen that the harmonic series is a divergent series whose terms approach 0. Show that 8, ...

A: Given :∑n=1∞ In1+1nClaim :To show that the series is diverges with limn→∞an=0.

Q: Consider the function f(x) = Complete the table below and sketch its graph. x 2 |-1 |-0.5 -0.1 F(x) ...

A: Given Data: fx=x+1x2+x

Q: a polynomial function is given  P(x)= x(x^2-4) describe the end behavior of the polynomial functio...

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Q: Find the area of R - region bounded by the curve y = 1/x2 and the lines y = x and y = x/8 O 1

A: Given: The curve y = 1x2 and the lines y = x and y = x8. To find: The area of the region bounded by ...

Q: lim COos x –1 x→0 x² – x³

A: To evaluate the given limit.limx→0 cos x-1x2-x3

Q: 3x+4 dx x²+3x+2

A: Let,I=∫3x+4x2+3x+2dxI=∫3x+4(x+2)(x+1)dxLet 3x+4(x+2)(x+1)=A(x+2)+B(x+1)3x+4(x+2)(x+1)=A(x+1)+B(x+2)(...

Q: Question Suppose that the piecewise defined function f is defined by S V4x + I, -8x? – x + V13 +75, ...

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Q: Consider the following matrices 1 1 -2 [ 1 | A В - 4 -3 1 -3 1 4 -3 1 2 -3 2 -3 4 Determins which of...

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Q: Find the area under the curve y=x3+3x2 and the x-axis between x=1 and x3D3. O 46 sq. units O 54 sq. ...

A: We need to find the area under the curve y=x3+3x2 on interval 1, 3.

Q: If h(x)= (-2+8x+8x^2) (7x+2x^6+7x^7) then h(x)=f(x)g(x) wher

A: Given that: h(x)=(-2+8x+8x2)(7x+2x6+7x7)

Q: Assume that the radius r of a sphere is expanding at a rate of 80 cm/min. The volume of a sphere is ...

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Q: t y = t dy Find dx 1 8t dy dx t dy Find dt dy dt + II II

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Q: Example 4 Video Example ) x2 + x - 3 Let y = Use the Quotient Rule to find y'. x3 + 8 Solution (43 y...

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Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled...

A: Given that: D(t)=4sin πt4+9π4+3

Q: show

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Q: Given f(x)=−3x^2−x+15, find f′(−3) using the definition of a derivative

A: We have given a function f(x) First we find f'(x) by using the definition of derivatives.

Q: For the curve whose equation is given by z -3xy +y-4x+2y+1-0, deline the equalion of the tangent lin...

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Q: Let f(x) = 8x + 10 – 3e². Then the equation of the tangent line to the graph of f(x) at the point (0...

A: The given function is: f(x)=8x+10-3ex

Q: e equation of the tangent line to the curve y = . at the point (3,- ) ) is x+16y +11=0 x+8y - 7 = 0 ...

A: Topic:- calculus

Q: 7 Show how to use the Intermediate Value Theorem to show that the equation 4 has a solution 1+z betw...

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Q: Drawing Example 1: Use the definition to find the derivative of the function f(x) = x? - 2x Solution...

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Q: SF S"(x² cos y – sin x) dxdy 2

A: Given that: ∫0π2∫0π(x2cosy-sinx)dxdy

Q: Problem 1: (1+ cos x) y' sin æ (sin r + sin x cos x – y)

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Q: The exam has 14 questions, and the total number of marks for the exam is 100. In how many ways can t...

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Q: Prove that the following integral can have any of the following 3 answers Ssen x cos x dx a) senx + ...

A: ∫sinx cosx dx multiply and divide by 21 2∫2sinx cosx dx=12∫sin2x dx    

Q: 4- Prove that lim- tan 2x 5-lim 2(-3+x)²-18) x-0 X-0 2.

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Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Write the correct u and du. 35 dx 3e 1. J- Ve3x...

A: Given query is to find the value of the integral.

Q: dy 6. Given that y(1) = -2 and dx = 3x + y, what is the approximation for y(2) if Euler's method is ...

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Q: Let 4 f(x) = (a + 4x + 4)* f'(x) = f'(5) =

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Q: (a) Estimate the area under the curve across the given domain with the "Trapezoidal Rule" using thre...

A: The integral to be evaluated using Trapezoidal rule is ∫x=-2x=+22x3+3x2-7x+3 dx. The trapezoidal rul...

Q: Let f(x) - 9 sin' a 4 f'(x)

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Q: In this question, we will use the notations A, B, and C to denote the angular measure of the interio...

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Q: n the coffee house will not make a profit. Determine what the coffee house needs to charge in order ...

A: As per our guideline we are supposed to be answer only first three subpart of questions you can repo...

Q: Describe the graph of the following systems of linear equations: 9x + 2y = -1 9x + 2y = 1 • a. depen...

A: Given that:   9x+2y=-1.   ....... (1)                         9x+2y=1.   ....... (2)