a. Let f (x) = sin(ax + b) and let g (x) = cos(ax + b) where a and b are %3D constants. Gues a formular for f*(x) and g*(x) for general n (positive integer )

Q: Given t2 – 1 - f(x) = dt 1+ cos?(t) At what value of x does the local max of f(x) occur?

A: Given that      f(x) = ∫0x[(t2-1)/1+cos2(t)]dt  Here we have to find at which value of x does the…

Q: 1. Find the convolution of f(t) = 3t and g(t) = sin2t?

A:

Q: 1. Determine the absolute extrema of f(x) = (sin r – 1) cos r on 2 2 if they exist, and identify the…

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Q: a. Let f (x) = sin (ax + b) and let g (x) = cos(ax + b) where a and b are constants. Gues a formular…

A: We have to find the f^n(x) and g^n(x)  Where f(x)= sin(ax+b)  and  g(x)= cos(ax+b)

Q: Given t2 – 4 f(x) = dt 1+ cos2(t) At what value of x does the local max of f(x) occur?

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Q: If f(x) = –3x + sin(47x) for x E [0, 1], find the smallest value of c E (0, 1) which satisfies the…

A: The Mean Value theorem states that for a continuous and differentiable function f(x) on the interval…

Q: V. Let z be a function of r and y, and tan y2 + x2 = z*ey. Solve for dz dz and

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Q: One of the followings is a harmonic function O a. u(x,y)=(x' - y' – 2x+1), O b. u(x,y)=(x-y - 2x+1),…

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Q: If f(x) = 5 sin x + 12 cos z, then %3D f'(x) = f'(2) =

A: The question has been solved in detail in the next step.

Q: 3 Use the definition 平grien FuncTionsEat'co,): for ー X+y X-ツ ix=ツ ) fory) =) singty4) ーty2 (x) #…

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Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(T/4) = 5? %3D

A: Given: f(x)=cx+log(cos(x))  and f'π4=5 find values c

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is f'(pi/4)=4

A: sol:-    Given f(x) = (x+ln(cosx)  differentiating ω. r.t   x, we get    f1(x) = c+1cosx(-sin x)…

Q: Suppose f and f' are differentiable functions of r. Given f' () = 0, f" () -1, and g(x) = log…

A: Differentiate two times at given value

Q: h(x) = sin² x + cos x О<x< 2л

A: We have to find the functional value at where either function is not differentiable or derivative…

Q: For the function f(x,y)= (x² + y²) tan(ln(xy)) + e(x-y) which of the following is the value of…

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Q: Let f(x) = (c + 1)x+ In(cos x). For what value of c is f'(/4)=6

A: This question can be solved using the concepts of differentiation.

Q: Suppose z is a function of x and y. Solve for dz if tan Vy? + x2 + z = z"e6y.

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Q: Given t2 – 1 dt 1 + cos²(t) At what value of x does the local max of f(x) occur? f(x): %3D

A: Part 1 of the Fundamental Theorem of Calculus : If  f(x) = ∫axg(t) dt then  f'(x)= g(x)

Q: Consider the following function and express the relationship between a small change in x and the…

A: Givenf(x)=10-acosxwhere a is constant

Q: Suppose f and f' are differentiable functions of r. Given f' () = 0, s" (÷) = -1, and g(r) = log…

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Q: Find the function that satisfies the given 4. f'(x) = 2 + cos x and f COS X = 1

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Q: Let z be defined implicitly as a function of r and y by the equation əz 4+ In (ry²) - cos (xy - z) =…

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Q: For the function f(x) = sin x , with the aid of elementary formula sin2A = 1/2 (1 − cos 2A), show…

A: Given that fx=sinxfx+y=sinx+yfx+y=sinx cosy+cosx siny by addition formulaNow ,       fx+y-fx…

Q: If S", f(x) cos(mx)dæ = } g ar cos(n²a) f(x) = Ln=1 nt +1 then m =

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Q: Given, f (x, y) = sin (x²y – 2x + 4). Find fy. - x cos (x²y – 2x + 4) x² cos (x²y – 2x + 4) O-x² cos…

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Q: Let f(x)= sin(x) – e¯*, po=0, and p,=1, then by Secant method p2=

A: f(x) = sin(x) -e-x  p0 = 0 and p1= 1

Q: Determine f such that (1, sin 1) is on the graph of f and e2z + 5e² + sin x ifæ 0

A: Given f'x=e2x+5ex6ex+sinx    if x&lt;01                           if x=0x5x2+1+cosx if x&gt;0 We…

Q: dz (2) Suppose z is a function of x and and suppose cos(32) xyz?. Find in Y, terms of x, y, and z.

A: The given function is, cos3z=xyz2

Q: find the aradients of the functions below a)f(x, y) = e-3y cos4x

A: We have to find

Q: If g(x) = f'(x) and if g(x) = (cos x – x sin x)e* cos x, then S g(x) tan(f (x))dx is

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Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: For the given function f(x) = cosx, let xo = 0, %3D X1 = 0.5, and x2 = 0.7. Find the value of…

A: From the given x=0.75, x0=0, x1=0.5 and x2=0.7. It is known that, the lagrange interplotation…

Q: Given ƒ(x) = √²; t² - 25 1 + cos² (t) At what value of a does the local max of f(x) occur? x = dt

A: Ans : x= -5     we use Leibnitz's Rule to solve this problems .

Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – z) =…

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Q: Given f(2) = . t2 – 1 dt 1+ cos?(t) At what value of x does the local max of f(x) occur? x =

A: Given the function

Q: Given that (1 COS 4.r) x2 a, if x = 0 if x 0. J 16+ Vx -4 If f(x) is continuous at x = 0, find the…

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Q: of the following function: ду Find the W = COS (x2 + 2 y) - e4x – z*y + y3

A: The given function is w=cosx2+2y-e4x-z4y+y3.

Q: Write out Taylor's formula around 0 of degree three, f(x) = P3(x) + E3(x), for f(x) = = COs x.

A: Given that fx=cosx. To determine the Taylor's formula around 0 of degree three. That is, fx=P3x+E3x…

Q: 25. If f(x) = (cos x)*, then %3D is k-0

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Q: -ツ() The function f(x) is invertible. Find given that f(x) = 5x +4 cos(x).

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Q: Find the general antiderivative of each of the following functions. i(x) = cos x/2

A: we have to find the general antiderivative of the given function f(x)= cos x/2

Q: a² f For the function ƒ(x,y), compute Or d0 if x =r cos O and x=r sin 0 .

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Q: Find and b such that the following function is continuous at x=( [x] – 2a x 0 -

A: To find the values of a and b

Q: a) Find the linearization of the function f(x) = cos(x) at a = π/2, b) Use a) to approximate…

A: (a) We have,

Q: b. Find y' of the following function using MATLAB y = sec(In(2M * x))e5x + cos(2Nx)

A:

Q: Let f(x) = 3 sin'x - 7 cos(2x), 0 <xS T. Find the interval(s) on which f is increasing. (A) (0, 7)…

A: Recall that, f is increasing on (a,b) if f'(x)&gt;0 in (a,b).

Q: d Prove, through the limit process, that (cos x) = - sin x. dx

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Q: Determine the value of a for which the function F(x,y) equation Fr - aFyy= 0. 8. cos(2x) cos(6y)…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.