The position of a particle moving along the æ-axis is given by s(t) = 8t2 + 6. Use difference quotients to find the velocity v(t) and acceleration a(t), filling in the following expressions as you do so: v(t) = lim [ h-0 , /h] = a(t) : = lim | , /h] = h-0

Q: Let f(x) tangent line to the graph of f(x) at the point (0, 0) is = 6x + 15 – 15e". Then the…

A: The given curve is: f(x)=6x+15-15ex

Q: Apply the Chain Rule to find the tangent line to f(x) = 4/2x – 6e²-*at x = 2

A: The given problem is to find the tangent line to the given function at given point x=2 Given…

Q: Use the definition of the derivative f'(x) = lim following functions. Show your step by step y = 2t*…

A: To find: The derivative of y=2t4-10t2+13t by definition of derivative. Given: The equation is…

Q: The position of a certain object (in feet per second) after t seconds is s(t) = (t+7)°, for 0<t< 10.…

A:

Q: For f(x) = x3, show that the slope of the secant line over [l,x] is x 2 + x + 1, and use this to…

A:

Q: On the curve y = x², find a point at which the tangent is parallel to the chord joining (0, 0) and…

A: To find the point

Q: Use the following definition of a derivative fla=lim f\x-f(a) x-- a x-a To find fa), where f x=x°-…

A: Given, f(x)=x3-2x  To find f'(a).  Solution: f'(a)=limx→af(x)-f(a)x-a      =f(a)-f(a)a-a=00

Q: Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 is y = -7x +2.

A: The derivative of a function at a point represents the slopeof tangent at that point .

Q: express the limit as a derivative.

A: Given limit is: The limit definition of a derivative is given by:

Q: Find the equation for the tangent to the curve at the given point using the limit definition of…

A: Find the equation for the tangent line to the curve at the given point by using the limit definition…

Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² – 7xy2 at the point (7, 8) z =

A:

Q: In the given equation as follows , determine whether the statement is true or false. If it is false,…

A: f is continuous function on [0,∞) and ∫0∞f(x)dx diverges

Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1). z…

A:

Q: Find the equation of the tangent line to the function f(x) = -3x2 – 2x at the point where x form y =…

A:

Q: Which of the following represents the slope of the tangent to f(x)=Vx+1 at x=8 ? Select one: 8+h-/8…

A: As we know that the expression for the slope of the tangent to the curve is:   limh→0fx+h-fxh…

Q: Find the equation of the tangent line to f-l x+4 at the point P (,0) for f(x) = 3x + 3

A: f(x)=(x+4)(3x+3)=x+13(x+1)+33(x+1)=13+1x+1 f'(x)=-1(x+1)2 f''(x)=2(x+1)3 the slope of the tangent at…

Q: Find the equation of the tangent line to the function f(x)=2x^2−9 at the point where x=−6. Give your…

A: Calculate the derivative of the function at given point than write the equation of tangent line.

Q: Since the tangent equation of f(x) = x^3 – x^2 + 3x – 5 drawn from the x = 1 apse point on it is y =…

A: Given : Function  f(x) = x3 – x2 + 3x – 5 Tangent equation on the given function f(x) at point x =…

Q: a point on the cor ve y=x² - 2x -3 at which is parallel to Find the tangent line the X-axis

A: Given query is to find the the point where tangent line paray to x axis.

Q: Use the limit definition to find the slope of the tangent line to the graph off at the given point.…

A: Given that ,  f(x) = 9x+9  at the point   (1,18) To find the slope of the tangent line to the graph…

Q: Find f (3) and f' (3), assuming that the tangent line to y = f (x) at a = 3 has equation y = 5x + 2.

A: Tangent to a function at a point is a line which just touches the graph of the function at that…

Q: Find the slope mm of the tangent line to the curve f(x)=x^3 at the point (1, 1) by using the…

A:

Q: Let f=sqrt(4x+3) and find the values below  1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x)/ h)…

A: Consider the given function

Q: Use the definition of the derivative (that is, f'(a) = lim sec(x) da to compute h+0

A:

Q: Why is the limit of the secant line PQ to a curve as it approaches zero is the same as the slope of…

A:

Q: Find the equation of the tangent line to the function f(x)=-3x^2-2x at the point where x=1. Give…

A:

Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² - 7xy² at the point (7, 8). z =

A:

Q: Find the point (x,y), at which the graph of y = 8x+6x-3 has a horizontal tanger The function y= 8x…

A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Given :               Whether the provided statement, "When the function y is differentiable,…

Q: Find f(3) and f'(3), assuming that the tangent line to y = f(x) at a = 3 has equation y = 5x +2.

A: Consider the provided function, y=5x+2 Find the value of f3  and  f'3 at a=3. y=5x+2 We can write…

Q: y = 3x?+1 ; (0,1)

A: Solution ) slope of the tangent line by the limit definition = m = (dy/dx) [ x = 0 becuase we have (…

Q: Find the equation of the tangent line to the function f(x)=2x2-x  at the point where x=−1. Give your…

A:

Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx

Q: Find f(4) and f' (4), assuming that the tangent line to y = f(x) at a = 4 is y = -6x + 2. %3D

A:

Q: Find the equation of the tangent line to the function f(x)=−2x3−4x2−3x+2 at the point where x=−1.…

A:

Q: दलालभ यला Find an equafion of the tangent line to the ceurve at the grven point. y=x3-3x + 1, (2,3)

A:

Q: Find the equation of the tangent line to the function f(x) = -3x – 2x2 – 1 at the point where x =…

A: Given : fx = -3x3 -2x2 -1

Q: Find the equation of the tangent line to the function f(x) = 2x? – x at the point where x form y =…

A:

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: Find the equation of the tangent line to the function f(x)=x3+3x2+x+4 at the point where x=−2. Give…

A: we have to find tangent line at x=-2given

Q: Find the equation of the tangent line to the function f(x)=−4x2−3x+2 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1given

Q: 2i Find the eguation of the tangent: lime to tul Cur ve y=4x -x* at the point (l,3).

A:

Q: Find the equation of the tangent line to the function f(x)=−3x3−2x2−1 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1

Q: On the curve y=x2 ,find a point at which the tangent is parallel to the chord joining (0,0) and…

A:

Q: On the curve y=x2,find a point at which the tangent is parallel to the chord joining (0,0) and (1,1)

A:

Q: For f (x) = x 3, show that the slope of the secant line over [ -3, x] is x 2 - 3x + 9, and use this…

A:

Q: If the tangent line to the curve y= f(x) at (5 , 20) is y = 6x – 10, then limh→0- f(5+h)–f(5) h…

A: For a function f the derivative at x=a is defined as f'(a)=limh→0f(a+h)-f(a)h. Tangent line to a…

Q: Q2/Find the following limits for the function y= f(t) graphed below: -2 I- -る | @ lim, fCt) = %3D O…

A: See the attachment