Find the derivative. dt 12) y = 5t + 6 - 5 1 1 C) 5x + 6 - 5 A) (5x + 6)2 B) 5x + 6 D) (5x + 6)2 36

Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

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Q: Find an equation of the line tangent to f(x) =3 at x 3. %3D OA. y=xln 3+ (1– 3ln 3) OB. y=27(xln 3 +…

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Q: Find the equation of the tangent line to y = 2"-5a -5x+1 = 4. at x = y = 12 In 2 - 1

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Q: Find the equation of the tangent line to the curvey = √2-4 at the point (5, 1). Oy=2-1 Oy= 22-2 Ov=z…

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Q: Compute the indicated derivative. U(t) = 5.3t2 + 5.3; U′(4) U′(4) =

A: Given: U(t)=5.3t2+5.3 Finding the derivative of the given equation : ddtU(t)=5.3ddt(t2)+ddt(5.3)…

Q: Find the equation of the tangent line to f(x) = 2x* – 5xat x = 1. - Oy=3x+10 Oy=6x+19 Oy=6x-9 O…

A: Given equation: f(x)= 2x4- 5x f(1)= 2(1)4- 5(1)= -3

Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized? |

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Q: (c) Compute the derivative of u = Vt² +2vt³.

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Q: Calculate the directional derivative direction Q(5,4) 4 3√-3x²-5xy3 of at P (1,-2) in the

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Q: Find the slope of the tangent line to the curve ((8x+9y)^(1/2))+((2xy)^(1/2))=7 at the point (2,1)

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Q: is the equation af tangent line at X=/ y = mx+b. to the giaph of f c) =x² -x at x=/ m%= b.

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Q: If ø = 4xy, find x and y components of the velocity at (1, 4) and (4, 4). Calculate the discharge…

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Q: Supose z is implicitly defined by the equation qy+ 3x + xyZ + 32=9 in an enmrament of the point…

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Q: Find all points on the graph of 3x 2 + 4 y 2 + 3xy = 24 where the tangent line is horizontal

A: Given:              3x2+4y2+3xy=24 We know the tangent line is horizontal when y'=0 So we want to…

Q: 8y If the directional derivative of f(x,y)%D at (2,1) in the direction of (2a,-3) is equal to zero,…

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized?

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Q: What is the derivative of k(y)=(6y^−1+3y^−2)(6y^−3+4y^−4)?

A: The given function is: k(y)=(6y-1+3y-2)(6y-3+4y-4) We have to find it's derivative with respect to…

Q: If =4xy, find x and y components of the velocity at (1,4)  and (4,4). Calculate the discharge…

A: Given that, ϕx,y=4xy    ...1. Let the points be, x1,y1=1,4 and x2,y2=4,4. Consider the velocity…

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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Q: Write the equation of the tangent line to f(x) = + In(a²) - 4 at x = 1. O y = 3x - 6 Oy = 4x - 7 Oy…

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Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: ) Find the directions in which the directional derivative of f (x,y) =4x2+sin (5 xy) at (1,0) has…

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Q: Find the slope of the line tangent to the x³ – 2x + 1 at x = 2 curve y %3D %3D O-10 O 1/10 O-1/10 O…

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Q: Find the gradent of x, y)-- and the largest value of the directional derivative of fx y can have at…

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Q: Compute each derivative. 4.3 1. dy (3r°y7-32r y3 + 5xy) 3x abc 2. Zz if z = 2x2ay

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Q: Find an equation of the tangent line for the curve.15 y + (xy + 2) = 0 at the point (3,-1) 3x-7y 16…

A: equation of tangent line at point 3,-1 for graph or curve xy+23+y2=0

Q: Make the curve y=ax²+bx+ c pass through (2,1) and be tangent to the line y=2x+4 at (1,6)

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Q: With respect to u, what is the derivative of: * 12 בV 2 2 dx Option1 Option3 -'/2 -15

A: Answer is mentioned below -

Q: The directional derivative of f=8x²y-2xy²+3z at point P(1,1,2) in the direction 2âg+2ây-âz is

A: First we find the gradient of the function f and then unit vector.

Q: Find the derivative using the definition fex)- = C fcx) fCx) = そり f ex) = KX" f cx) fx) = gx).hcx) 9…

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Q: Find the derivative: y = (3x² – 2x) Væ5 – 2x + 2 27 –14a5 –30z² +36x –8 2y5 -2x+2 dy %3D dæ 27+15* –…

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Q: Compute the derivative of g(æ) = e dt. 22 -2xe -2xe O -2re

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Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: 3. Apply definition (3), Sec. 19, of derivative to give a direct proof that dw dz 1 when w: Z (z =…

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Q: Find the equation of the tangent line on 3xe™v² - ez 2ye at (1,1)

A: Given  3xexy2-ex3=2yex2first we find dydx at point (1,1)

Q: Use the definition of the derivative to compute dy/dx. y=2x^2-3x+1

A: Use the definition of the derivative to compute dy/dx. y=2x^2-3x+1

Q: calculate the required derivative using the chain rule. z.ton"() -1 - tan u =Y Cose » yarsin@ az -?…

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Q: Find the derivative ofy. with respect to x if y=(Ix +5) (9x² +2x) %3D

A: Given that: y=(x+5)(9x2+2x)

Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

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Q: Find all (x,y) points where x² +4y² +4x- 8y+4 = 0 has horizontal or vertical tangent lines.

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Q: at dz = (4자) 424-4%.

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Q: Find the equation of the tangent plane to z=6x2+2y2  at the point (1,5)

A: Given  z = 6x2+2y2  at the point (1,5)

Q: Compute the derivative y = dy %3D dt 2t - 7 y = 7t- 3

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Q: Find the equation of the tangent plane to z= 6x +2 at the point (1,5).

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Q: Find the slope of the tangent line to V3x+ 4y= 5 at point (3, 2) %3D Onone of the above O-1 03 O-2…

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Q: Confirm the approximations by using the linear approximation at x = 0

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.