QI: Show that the following functions satisfy C.R.E f(z) = sin z

Q: The range of the trigonometric function f(x) = sin (x - 5 is aY-0o, +0) b) [-1,1] c) [0,2] d) (–1,1)…

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Q: sin(x – y) cos x sin y tan x cot y – 1 Prove the identity:

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Q: describe the domain and range of the function. g(r, s) = cos−1(rs)

A: Given, g(r, s) = cos−1(rs)

Q: Consider the function defined by f(z) e sin z. %3D Find f") Give an exact answer.

A: Consider two differentiable functions fx & gx. The product rule of differentiation is given by:…

Q: Show that the functions f and g are identically equal.

A: Given functions are -  f(x) = sin x . tan x g(x) = sec x - cos x We have to show that f and g both…

Q: Consider I x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? O 1/4…

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Q: Find f. f ''(θ) = sin(θ) + cos(θ),    f(0) = 5,    f '(0) = 1

A: given, f ''(θ) = sin(θ) + cos(θ),    f(0) = 5,    f '(0) = 1 to find f.

Q: X. C. Prove the following identities. sin(u – v) 12. sinu sinv = cot v-cotu

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Q: The range of the trigonometric function f (x) = 1 + cosx is COSX IS a) (-∞, +∞) b) (-1,1) c) [0,2]…

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Q: y = a sin (x + b) u sin (x + b) -a sin (x + b) O a cos (x + b) O -a cos (x + b)

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Q: Find f. f"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4

A: Given functionf"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4we have to find , f(θ)

Q: Show that the functions f and g are identically equal.

A: We have  fx=cosx.cotx and gx=cscx-sinx Then, fx=cosx.cotx=cosx.cosxsinx=cos2xsinx And…

Q: Show that the functions f and g are identically equal.

A: Given: fθ=1-sin θcos θ-cos θ1+sin θgθ=0 To Find:  To show that fθ ang gθ are identically equal.

Q: f (x) = 3 sin x + 3 cos x, [0, 27]

A: Consider the function: fx=3sinx+3cosx Differentiate the given function with respect to “x” then,…

Q: sin(z) = e-e 2i elz-e-iz ekte-iz 2i - 2i

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Q: cos(t) t4 COS f(t) =

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Q: Consider the function sin? cos X – X X + X f(x)= Vx -1 sin Determine f'(0.25) using 3 point central…

A: Given: fx=sin2x2+xcosx-xsinx-1x2+1 h=0.01 To find: The value of f'0.25, using 3 point central…

Q: Q:Findthe domain of the following functions sin 'x (1) s''x (i) [x] 1 (ii)- | x | ,× cos 'x

A: In this question, we need to find the domain of the given functions.

Q: sin (x) с. у c. y =: 1+cos (x)

A: Given :- y = sin(x)/(1+cos(x))  To find Second derivative of given function

Q: d. f(x) = sin (cos*x)

A: Given :- f(x) sin5(cos4(x))  To find:- Derivative of f(x)

Q: Is the function A cos (ka - wt = psi) a function of the operators ^ E and ^ T?

A: yes this is true

Q: The function f(z) = e-y sinx is harmonic function True O False O O

A: A function f is said to be harmonic function if it is satisfied Laplace equation

Q: a) Find f'(x) for f(x) = sin?x · tan³((x² – 3x + 1)5). %3D (tan*/x) (sec²x) dx h) Evaluate

A: We have to find the derivative of f(x).

Q: SI sin A+tan A = sin A %3D 1+ sec A +sec.

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Q: What is the range of f(r) = cos(x)? i) [–1, 1] ii) [0, 1] iii) (-∞, ∞) O i O i

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Q: sin (z+27) .A sin z .B COS Z .C tan z

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Q: Find f. f ''(?) = sin ? + cos ?,    f(0) = 1,    f '(0) = 3

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Q: Which one of the following functions is harmonic function? O (A) h(x, y) O (B) h(r,y) =e" cos y +…

A: As we know that for harmonic function hxx+hyy=0

Q: f(r) = 5 sin(sin(x)) %3D

A: answer is in next step

Q: Consider the function defined by f(z) = sin z cos 3z. Find f" () Give an exact answer.

A: We know that, product rule of differentiation states that ddxfx·gx=fx·g'x+gx·f'x            ⋯⋯1 We…

Q: The range of the trigonometric function f (x) = 1 + tanx is a) (-0, +0) b) (-1,1) c) [0,2] d) [-1,1]

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Q: Let fla) =Sint () Find f'(a) Let fla)= sin (u4) , Find f'Ca) Find f'(a) ニ

A: We can make it easier for you

Q: (a) Find F'(x), where (i) F(x) =x t cos(r²) dr; - [ (ii) F(x) = sin(e") ds.

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Q: 1+ sin r , r < 0 f(x) = COs a sin x

A: Now, check the function is continuous at x=0 or not. Thus, the function is continuous at x=0.

Q: Sketches of y=sinx,y=cos× and y=tanx on separate sets of axes if xe(0°;360°)

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Q: Describe how csc t varies as t increases from 0 to T/2. R (0, 1) cot t Q P(x, y)t units t radians…

A: let y=csct and t∈0,π2 claim- to determine how csct varies as t increases

Q: f(x) = a cos(bx) а cos

A: Given,                         f(x)=acos(bx)+cx+dif a=6, b=0.5, c=3 and d=4.

Q: sketch the function y(t)= cos 5t

A: The  period of y(t) = cost  is 2π The period of y(t) = cos5t is 2π5   so the graph of y(t) = cos5t…

Q: A. sin X = sin Y %3D B. cos X= cos Y C. tan X = tan Y D. sin X = cos Y %3D

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Q: Let f(x, y) = tan-(y/x). Find and simplify f. and fy. Then find and simplify feæ, fry, and fyy-

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Q: Find f. f ''(?) = sin(?) + cos(?),    f(0) = 1,    f '(0) = 2 f(?) =

A: Given the second derivative of a function f"(x)=sinx+cosx And initial conditions f(0)=1,f"(0)=2

Q: Consider the function defined by f(z) sin z cos 3z. %3D Find f" () . Give an exact answer.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Consider the function. y = -7 sin-(x) (a) Decompose the function in the form y = f(u) and u = g(x).…

A: We have a function to find part (a) and (b).

Q: QI: Find dyldx for the following functions:- (3) y = (tan x)tnz+ t (4) y = sin-(x² +x) + 5" %3D

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Q: Determine whether the given functions are harmonic or not. If they are harmonic functions, find for…

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Q: Determine the function f satisfying the given conditions. f ' (x) = sin(x) cos(x) f (2π) = 7 f(x) =…

A: Given,