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

Q: What is the range of the function f(x) = 2 cos x + 1? [0,3] O[-2,2] O[-2, 1] O[-3,0] O[-1,3]

A: f(x)=2cosx+1

Q: -1 What is the range of the function y = cos ( +1)? 이[-2,이 O [0, T| T o (0, 7)

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Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: 2 x+1 2) Evaluate f,“ dx using the substitution u 3 Зх — 2 V3x-2 3) Evaluate f2 e cosx dx

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Q: What is the range of f(x) = cos¯¹(0)? A [-] 2 2 B [0, π] C [-1,1] D (-∞, ∞)

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Q: 1] Evaluate (a) -S (s²+1) ² {t sin (b) S 1/2 5² (s² +¹)² (d) S

A: Find Laplace of tsin(t/2)

Q: 28. Let f be the function given by f(x) = 2 cos x + 3e. What is the value of f'(0) ? (A) -3 (B) 0 3…

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Q: Determine if the setsin² {sin²x, 1-cos(2x)} is linearly dependent or linearly independent on I =…

A: Let B={sin2x,1-cos(2x)}.

Q: Let u(x,y)=4x+3x2y−y3. Part (a) Show that u is a harmonic function. Part (b) Find a harmonic…

A: The given problem is to show that the given function u(x,y) is harmonic function and also to find…

Q: O [-5, -1) U (1,6] O (-5,6] O [-5, 6] O (-5, -1] U [1, 6] Find the domain of r(t) = (ln(t + 5),…

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Q: Discuss the difference between harmonic and conjugate harmonic function. Also find the analytic…

A: The given problem is to discuss the difference between harmonic and conjugate harmonic function and…

Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

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Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

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Q: Determine whether the given set of functions is linearly independent on the interval (-co, co).…

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Q: Evaluate sec³ (0) tan³ (0)dē. ○ sec (0) - sec³ (0) + C ○ sec³ (0) + sec³ (0) + C O sec³ (0) + sec(0)…

A: Step 1:To solve the integral ∫sec5(θ)tan3(θ)dθ, we can use substitution and trigonometric…

Q: The function y = (x- 1)(x-2)(x - 3) is negative on the interval(s) %3D O a) xe (-0, 1) and x e (2,…

A: We have y=x-1x-2x-3 First, we find the critical points by letting y=0: y=0⇒x-1x-2x-3=0⇒x-1=0, x-2=0,…

Q: a) The function f: x 1→ a +b cos x, is defined for 0 <x< 2n. Given that f(0) = 10 and that f ( n)=1,…

A: Hera function is given and we need to find the value of a b and the range of function

Q: v=e2r-y cos (y– 2x) Obtain the value of of the relation дхду A 8e2r-y sin (y– 2x) B - 6e2 -y cos(y–…

A: Option (C) is the correct.To solve this question first we take the partial derivative with respect…

Q: If v(r, y) is a harmonic conjugate of a harmonic function u(x, y) show that the function g(r, y) =…

A: Harmonic function: A two variable function ux, y is said to be harmonic, if the function is twice…

Q: 3. (a) Let f(t) = t – sin t for all t. Show that f is a strictly increasing function of t, and…

A: f(t) = t - sint for all t  So, f'(t) = 1 - cost for all t  &amp;, f"(t) = sint for all t

Q: (b) (sin 0)y"+ (0+ cos 0)y" 2tan@

A: Given: sin θy'''+θ+cos θy''=2 tan θ (a) The number of the highest derivative in a differential…

Q: = csc() – y] dæ + ædy = 0 C CSC Dy = = cos-' (In z + C) O Ina + cos () = C O Inz (금) =C cos Oy = x…

A: Topic:- application of integration

Q: Match the function with its range. f(x) = x2 + 1 - 1 [-1, 0) O [0, c0) O [1, 0) O (-0, 0) U (0, o) O…

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Q: A graph of f (z) =a cos(br) is shown, where b is a positive constant. |(0, 4) (T, 4) |(27, 4) -2…

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Q: Let h(x) = tan(2x + 7). Then h' (3) is and h'' (3) is

A: Given query is to find indicated derivative

Q: . What is F(/3) if C = 0?

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Q: -tan (m + 1)(x) + C tan I + m um + ( x ) (x + ₁)² I m+3 1 с

A: Using substitution then integrating we get correct answer as (C)

Q: -y If u=x² - y² and v= x* +y then A) u is a harmonic function B) v is a harmonic function C) f(z) =…

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Q: The evaluation of fet tan(et) dt O sec2(t) + c O -tan2 (e-t) - 1+c C sec? (e t) + c c tan? (et) + c…

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Q: [s sin x cos x esin²x+dx = A B C D - sin x cos x esin²x+ esin²+ + C 1/2 (sin ²x + 7) + C e -…

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Q: What is the range of f(x)-¹ = cos¯¹(0)₂ A C D [-] 2 2 [0, π] [-1,1] (-∞, ∞0)

A: Given query is to find the range of the function.

Q: Tan x = 2, x E [0,π\2]

A: we have to find value of x, in  tanx=2 where x∈0,π2