If a function f(x) = ax³ + bx2 + cx + 1, where a, b, c are integers and a > 0 is such that %3D f( sin 18 = 0. Find the value of f(1).

Q: If f(x)=2 sin x/1+cos x, then f′(x) =    f′(4) =

A: We have to find

Q: 1. f(x) = 2x2 – 3x+4 2. f(x) = e-2x sin 5x %3D

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, f(x) has a root in [o,. If we use…

A: f(x)=cos(x)-3x+1 secant method iteration formula xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn) given x0=0.5,…

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = cos x −…

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Q: Suppose z is a function of x and y. Solve for ∂z/∂y if tan √(y^2 + x^2 + z) = z^(x)e^(6y).

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Q: If fx*cos x dx = f(x) - j2xsinx dx, then f(x) is A. 2 sin x + 2x cos x+C B. xsin x +C %3! C. 2x cos…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

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: b) [F(x) then find f(x). If 3 In(x)/ sin(3x) − 3e³ + x² + 3. - f(x)dx= 3 ln([x]) + 3x + C

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Q: It is known that the range of the function f(x)= a sinx+1 for xER is -2<f(x)≤4, then a = ?

A: Given fx=asin x+1,     ∀x∈ℝ range of fx is -2≤fx≤4

Q: 4. Given f(x)= sin 6x cos 6x dx , what is f| | if f(0)= x ? A. π В. О С. 2л D. — я

A: This integration can be integrated by using substitution method. Clearly it is observable that put…

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: If f (x) = – sin(x), then f (10) (x) is equal to A - sin(x) В - cos(x) C sin(x) D cos(x)

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Q: Find the critical numbers of the function. g(x)%3D8X+sin 8x

A: Given query is to find the critical numbers for the function.

Q: 17. Derive A) f(x) = 10x* –- 32x + e² %3D B) y = e-* sin x

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Q: Find the best quadratic approximation to f on the interval [ 0, 1].                   f(x) = sin(…

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Q: Find constants c1 and c2 such that: F(x) = c1 sin(3x) + c2x cos(3x) is an antiderivative of f(x) =…

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Q: (sin 2x)y' = y cos 2x

A: Consider the given Differential equation, sin2xdydx=ycos2x divide both side of the differential…

Q: If g(x)=cos2x and f(x)=sin (1/2) (π), find g(f(x))

A: Given functions are  g(x)=cos2x and f(x)=sinπ2

Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

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Q: If the function = (x)S x' +1 cos( 2 7x - a) if x < -1 is continuous at if x 2 - 1 x = -1 , find the…

A: Given: fx=cos2πx-aifx&lt;-1……1x3+1ifx≥-1……2   To find: Value of a where fx is continuous at x=-1.

Q: If ¹f [ 2³ sin ædæ = −2³ cos x + 3x² sin æ+ 6x cos a - 6 [ f(x)dæ, then f(x) = a. x cos x b. sin x…

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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: Determine the root of F(x) = 7 sin(x)e¬* – 1 using secant method with 3 iterations given Xị-1 = 0.5…

A: Given that, F(x)=7sin(x)e-x-1

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (₹) < 0, ƒ (x) has a root in [o,]. If we…

A: In secant method the next approximation root may or may not lies in the previous two roots

Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

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Q: Use the graph of sin x/cos x to find all values of x between x =0 and x = 4t f %3D true: a. sin…

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Q: This problem deals with functions defined by f(x) =x + b sin x, where b is a positive constant and…

A: Given,   f(x)=x+b sin x  y=x+b :-Tangent to f(x)

Q: If f(x) = 6 sin x + 10 cos x, then f'(x) = f'(4) =

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Q: 2. If f(x) = 2x – 1 and p(x) = = cos (x). Find x, for 0 < x < 2n, if (f •p)(x) = -2

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Q: Consider the function f(x) = cos x -3x+1. Since f (0)f () <0, f(x) has a root in [o]. If we use…

A: Given that                     f(x)=cos x-3x+1 Newton-Raphson iteration scheme is…

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (1) < 0. f(x) has a root in - [o,]. If we…

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Q: 2. f(x) = sin x [0,21]

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Q: ,1 x² - 4x⁹+ A) True B False sin(x) (1+x²)² |dx=0

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Q: given f (x) = 3/5 cos (6x), what is the largest possible value for f (x)?

A: Given query is to find the largest possible value of the function.

Q: If f (x) = - cos(x), then f (0)(x) is equal to A - sin(x) B - cos(x) В © sin(x) D cos(x)

A: We have to differentiate the given function 9 times

Q: If y = (x – a)/2ax – x² + a² sin¬'(÷ prove that y' = 2/2ax – x² a is constant.

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Q: If f(x) = 4 sin '(2), f'(x) =

A: The given function is f(x)=4sin-1x5  .................................... (1)

Q: . Consider the function ƒ(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ(x) has a root in [o,]. If we…

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Q: Consider the function f(x) = cos x − 3x + 1. Since f (0)ƒ () <0, f(x) has a root in [o,]. If we use…

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Q: Use the Intermediate Value Theorem to show that sin x x2 – x has a solution on the interval (1, 2).

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Q: Consider the function f(x) = cos x − 3x + 1. Since f(0)ƒ () <0. f(x) has a root in - [o,. If we use…

A: We have f(x)=cos(x)-3x+1,  x0=0.5, x1=0.6 then secant method formula:…

Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B }sin'x + C {c}-cos'x + C {D} sin 2x + C

A: Given query is to find the incorrect option for the integral.

Q: Find the value of c that makes the function continuous at x = 0.

A: Given function:

Q: If f(x) = 2sin (3x), the formula to compress the graph vertically by factor 4 %3D followed by a…

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Q: If ef (x) + [ f (x) + 1] = sin x andƒ(0) = 0, find f'(0).

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Q: Find the general solution of the following first-order ODE xy' = y + 2x' sin² (2)

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