Determine whether the following statements are true and give an explanation or counterexample. d. a. dx (sin ?x) = cos ?x b. d? 5(sin x) = sin x dx2 c. (cos x) = cos x d. The function sec x is not differentiable at x = dx 2°

Q: Find the PDE that is satisfied the following function u(x, t) = e' cos(x) %3D

A: Given function,  u(x, t) = et cos (x)  To find the partial differential equation.

Q: Which of the following functions does not have the property that f(x) = f(4(x) ? A flx) = cosx B…

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Q: Because f(t) = sin t and g(t) = tan t are odd functions, what can be said about the function h(t) =…

A: Given functions are: f(t) =  sin t g(t) = tan t Since we have, f(-t) = sin (-t) = - sin t = - f(t)…

Q: Find for the following function. xp y= 3x cos x sin x dx

A: Given the functiony=3x2cosxsinx

Q: If (x) = tan(e"), then f"(x)= %3D A. 2e sec (e") B. 8e tan(e") C. 4e sec (e") D. 8e" sec (e*)tan(e")…

A: Given, f(x)=tane2x

Q: Evaluate the following integral. 1/6 | (sec x – cos x) dx 1/6 - 2/31+ 11 8/3 (sec x- cos x) dx =…

A: Given that: ∫0π/6(sec x-cosx)2dx

Q: Given the function f(x,v) = *ye6-sin²x e cos?x The second derivative f, of f is equal to 0. Select…

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Q: Make a table of values using multiples of t/2 for x between 0 and 47 for the function y = x sin x.…

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Q: Q2\ Answer TWO branches only A- Prove that sin(tan¬1(x)) V1+x? sin-1(x2) ) B- Find for y = sech ( dx…

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Q: Given f(x,y) = 3x sin(4xy). Find fxy(4,5). Give you answer correct to two decimal places. Answer:

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Q: Given f(x,y) = 5x sin(5xy). Find fxy(3,3). Give you answer correct to two decimal places. Answer:

A: Given :       f(x,y)=5x sin(5xy) To find : fxy(3,3)

Q: Explain the relation between the following two formulas (c is a constant): d sin(cx) = c cos(cx), dx…

A: If the derivative of a function f(x) is known then the derivative of f(cx) can be calculated using…

Q: If ſ x sin x cos x dx = xsin²x + Ax + B sin 2x + C, what is the value of A + B?

A: The given integral is, ∫xsinxcosxdx=12∫x(2sinxcosx)dx=12∫xsin2xdx=12∫xsin2xdx=12I1

Q: h(x) = cot (e*) y = sin vx3 + 1

A: The given function is hx=cot3ex. h'x=ddxcot3ex=3cot2exddxcotex=3cot2ex-csc2exddxex=-3excot2excsc2ex

Q: Given f(x,y) = 5x sin(3xy).  Find fx(4,2). Give you answer correct to two decimal places.

A: fx(x,y) is partial derivative of f w.r.t x

Q: Evaluate each of the following. a) o sec?(x) tan (x) dx b) |x – 5| dx c) /x Vx² – 1 dx -

A: “Since you have asked multiple question, we will solve the first question for you. To get remaining…

Q: Given f(x) = 2x(sin x + cos x), answer the following: %3D a) f'(x) = b) f'(5)

A:

Q: Given f(x,y) = 5x sin(3xy). Find fxy(4,2). Give you answer correct to two decimal places.

A: Given: f(x,y) = 5x sin(3xy). We have to find fxy(4,2).

Q: Determine whether the following statementsare true and give an explanation or counterexample.The…

A: Given functions are p(x)=sin3x and q(x)=4sin3x.

Q: f(x) 16 %3D = +- - 11x 2

A: 1. Rule of derivative of sum and difference of two functions states that ddxg±hx=dgdxx±dhdxx. Use…

Q: Which of the following is true about the DE y" + y = tan (x), where A and B are constants? (Choose…

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Q: Č) ´It is given that f(x) = tan¯"(1 +x). (i) Find f(0) and f '(0), and show that f "(0) =

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Q: that y?=x+ sin Cxy) - T 2 and let ß Be the value of dy evalwated atlxy

A: Given- y2=x2+sinxy-π24 To Find- The value of dydx at π2,1 and considering that value as β and then…

Q: - Given the function f(x, y, z) = x ln(1 – z) + and simplify your answers. a) fa b) sin(x - 1) 2y…

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Q: Answer the following True or False, sin dt 圭 dt 0. 1 t? t cos O True O False

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Q: e cos xy [ydx + (x + tan xy) dy] = 0 %3D

A:

Q: Q2: Derive the following functions sin2x 1. f(x) sec?x 2. f(x) = x²e*²

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Q: Determine if the following statement is true. If it is false, explain why and correct it. For each…

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Q: Given that z and w are independent variable and dependent variablerespectively, obtain dz/dw a)…

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Q: t/2 Evaluate using Wallis' Formula: sin? x cos5 x dx

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Q: At which of these x-values is the value of y=cos x greater than the value of y=sin x? Select all…

A: From above we can see that when x=π6, (cos x,sin x)=32,12 here cos x> sin x From above we can see…

Q: Evaluate each of the following. a) sec (x) tan (x) dx b) |x – 5| dx + c) /x Vx? – I dx -

A:

Q: Find of the following functions. [ dr (a) y = sec(7?) (b)y = sin7x + cos5a

A: here we can find the derivative as below.

Q: Solve the following Riccati equation dy _2 cos? x – sin² x + y² 2 cos x y1(x) = sin x dx

A:

Q: Explain the relation between the following two formulas ( c is aconstant):

A: Consider the provided formulas, ddxsincx=ccoscx   and   ∂∂xsinxy=ycosxy Explain the relation between…

Q: Now evaluate f(x) for x = 4n. 47 f(4t) = sin 4 Therefore, the possible point of inflection is as…

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Q: Find dx or y' of the following functions and make any a. y = cot(Ve" ) tanh(e") b. Y =…

A: taking ln both side

Q: SF S"(x² cos y – sin x) dxdy 2

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

Q: ,determine f(t−a)for the given function f and the given constant a. Q. f(t)=e−t(sin2t +cos2t), a…

A: f(t)=e−t(sin2t +cos2t), a =π/4. We need to calculate f(t−a)for the given function f and the given…

Q: Evaluate the following: 1) f sin x sin(cos x) dx

A: Integration

Q: Suppose z is a function of x and y, and tan Vy? +x² = ze6y. Solve for and dx ду

A: Here, given that z is a function of x and y and tan y2+x2=zxe6y⇒tan y2+x2=ex ln ze6y...(1)

Q: T/2 Evaluate using Wallis' Formula: sin? x cos5 x dx

A:

Q: (b) Evaluate the given trigonometric integral sin r dx (x² + 1)(x² + 9)

A: The given integral is ∫-∞∞sinx(x2+1)(x2+9)dx. It is of the form ∫-∞∞f(x)g(x)sin(nx)dx. To solve this…

Q: Find of the following functions. Do not simplify. dy da (a) y = x³ cos(Tx) (b) у (3x–10)² sin(x) Y =…

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Q: Using an appropriate substitution, f sinº (x)cos'(x)dx is equal to: cosl +C 11 cos 11 O Ths opton O…

A: We will find the integral by substitution as following-

Q: Given [f (x)dx = F (x)+c, if F(x)= /cos (2x), find f (x). %3D

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Q: Which of the following statements is true? @ Soue(x*) dr= - coa(x) +c x²+2 - dx =x+ tan(x) +C x²+1…

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Q: Evaluate the following: 2Tt sin x cos x dx a) S"Isin? x cos x| dx 0. b)

A: ∫02π(sin2x)(cosx)dx Let u = sinx du = cosxdx ∫02π(u2)du u3302π = sin3x302π sin32π3 - sin303  0

Q: Let f (t) = et sin 5t

A: