BE F(t) = (cos(at), sin(at)) e G(t) = (eat, e-at), wiTH a > 0. CHECK IF a) F"(t) = -a²F(t)ANDf"(t) = a²G(t). b) F"(t) · F(t) < Q NG"(t) · G(t) > 0.

Q: The lowest point on the graph of y = cos x, 0sxs21, occurs when x=

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Q: Evaluate e sin x cos x dx using Simpson rule with h 20

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Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: Preview and where B is: Preview

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Q: , Suppose that the tangent line to the graph of f(x) = xlb) at r = 1 is equal to the tangent line to…

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Q: Is there a function f(x, y) such that fx : one. If not, explain the reason = e* cos y and fy : = e*…

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Q: Find the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in in the…

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Q: The slope of the tangent line to the curve at the point where x = O +1 -1 DNE f(x) = sin² x cos²x

A: The slope of the tangent line to the curve  y = f(x) at the point x= k is f '(k)

Q: 14. S 5 sin 3x cos 3x dx 15. ſ tan? Ode

A: We can solve the given integral as follows:

Q: Consider the function y = sinh 2x + 1. Which ?one is a critical number of this function

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Q: f(x)% 3D tanh In(2x) is equivalent to

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Q: Differentiate y with respect to x where y= cos(-3x2)

A: Differentiate y with respect to x.

Q: 13. We know that x = r cos 0 and y = r sin 0, then find the derivative af/ar if 1 f = ? + y?

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Q: Find the derivative of cos(0)d0. du Jo cos(0)de = cos (w²) · 2w • d de So" cos(8)d0 = cos(2w) • d S…

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Q: Find the line tangent to the graph of f(x) = cos(x) at xo = T.

A: f(x)= cos(x)  Then, f(π) = cosπ⇒f(π) =-1

Q: The linear approximation at x = 0 to sin(3x) is A + Bx where A is: Preview and where B is: Preview

A: Given function:

Q: Find f'a) for f(x)= =Sinx 1- Cos X %3D

A: We have to find the derivative of the given function.

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

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Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

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Q: The linear approximation at x 0 to f(x) = sin(6x) is:

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Q: Given: f(x) = / (2 – 4t) sin() - dt %3D tan(2r) 17 – cos(2nt) Find the equation of the line tangent…

A: The tangent is a straight line to a curve that touches the curve at exactly one point. The point…

Q: Let z= sin (y²– 4x). Find the rate of change of z with respect to x at the point (2, 1) with y held…

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Q: A particle moves along the x-axis with velocity given by v(t) = 6T sin (2nt) for time t > 0. If the…

A: Given: vt=6πsin2πt at t = 1, x = -4

Q: Find the derivative f (t) = 1- cos t | a. 1 cos t - 1 sin t C. 1– cos t - t · sint (1 – cos t)? b.

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Q: Find the most general antiderivative of the function. f(x) = 5 cosx-7 sinx

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Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: Find constants c1 and c2 such that F (x) = c1 sin 3x + c2x cos 3x is anantiderivative of f(x) = 2x…

A: Given: Fx=C1sin3x+C2cos3x and the antiderivative of F(x) is fx=2x sin3x To find the constants C1 and…

Q: Q4: To evaluate the integral cos x dx using the reduction formula of cosine function

A: We know that reduction formula for  ∫cosndx=1ncosn-1(x)sin(x)+n-1n∫cosn-2(x)dx Now we will solve…

Q: Find the value of parameters € and ¶ that makes f(x)=€x+¶ if x&lt;0 and f(x) =2(¶+€)sin(x) +…

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Q: Show that sin x dx=1-cos t (0<x<t<}r).

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Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in the form y =…

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Q: Is the function h(x) = 3 cos x+ sin x concave up or down at the point 3 я?

A: Given:

Q: Find an approximate solution, accurate to 5 decimal places, to the equation cosx=x2 that lies in the…

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Q: f(x) = cos (In (3x))

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Q: 2. Show that the LT of sin(wt) is L sin(wt)] (s) where w is a positive constant.

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Q: ) Given the function f(x) derivative f"(1) with h, h/2 and h/4. 5. e Vx cos (Tx), approximate the…

A: Given function is  For this answer, we choose  We have  (up to 4 decimal place accuracy) We also…

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: 2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log…

A: First find the domain of f1x=cos-12x1+x2: The domain of cos-1x is -1,1. Therefore, -1≤2x1+x2≤1 Now,…

Q: The linear approximation at x = 0 to sin(6x) is A + Bx where A is: Preview and where B is: Preview

A: First of all, consider the formula to find the linear approximation at any point a for function any…

Q: Find a function whose 2nd antiderivative is f(x) = tan(x) + 4x+1

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Q: Find dy if sin x + 1 = cos y dx²

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Q: Use the trapezoidal rule withn= 4 to approximate cos(x) dx Keep at least 2 decimal places accuracy…

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Q: A particle moves along the x-axis with velocity given by v(t) = 3T sin (t) for time 10 at time t =…

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Q: We know that x =r cos 0 and y =r sin 0, then find the derivative af /ər if 1 f = x2 + y2

A: Given f = 1x2+y2  and x = r cosθy = r sinθ Thus f = 1r cosθ2+r sinθ2= 1r2 cos2θ+r2 sin2θ=…

Q: Find an equation of the tangent line to the graph of {(=) = [. t cosh (t² – 1) dt f(x) /1+ln (x)…

A: First I have written the rule of derivative of an integral to find the slope of tangent line for…

Q: Use a linear approximation of f(x)=cos(x) at x=5π/4 to approximate cos(222∘)

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Q: For which  x value(s) is the function  f ( x ) = sin ^− 1 ⁡ ( 2 x )  defined and not differentiable?

A: Given that the function is       f(x) = sin-1(2x)  Here we have to find those values of x, in which…

Q: Find for the following function: dx 4- y = In2 5- tan-1 V4x - 5

A: Topic : differentiation