Assume that f(x) is everywhere continuous and it is given to you that f(x) + 7 lim %3D х — 6 х—6 It follows that y = is the equation of the tangent line to y = f(x) at the point ( ).

Q: If a is a positive integer, then the slope of the tangent to the graph of y = a²x – a ln(ax +1) at z…

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Q: Given that the line y= 2x +c is a tangent to the curve y = kx, where c and k are positive constants…

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Q: 9. Find the constants a, b and c of cubic function f (x) = ax³ + bx + c such that : • The slope of…

A: Given that, f(x) = ax3 + bx  + c Slop of tangent line at x = 3 is 0. f'(1) = 24 f(x) croses the x…

Q: Suppose z is a differentiable function of x and y implicitly defined by the equation E : 23 + xe² =…

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Q: Let y(t) be the solution of dy/dt = 0.3y(2 − y) with y(0) = 1. Determine limt→∞ y(t) without solving…

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Q: Find the length of the curve y = In sin x from t = -2 to t = 0.

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Q: e-i.dt = lim X+ 00 V TE 0, Select one: a. b. NOT C. 8, O d. 1 O e. 0

A: According to our guidelines we can answer only first question. In first question we use the concept…

Q: Complete the table. (Round your answers to four decimal places. If an answer does not exist, enter…

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Q: 4. Find the equation of the tangent line to f = 10** at x = 0. А. у %3D 1 B. x = 1 D. y = x – 1 E. y…

A: Tangent line equation =>y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate…

Q: Let f(x)= 9 sin x/ 2 sin x + 4 cos x Then f'(x)= The equation of the tangent line to y=f(x) at a =…

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Q: 7) What is the equation of the tangent line of f(x) = xe"+ 3, at x = 0 a) Y= x+3 b) Y= 3 c) Y=…

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Q: Use Euler's method to make the graph of the following functions on the given interval. a) dx/dt = t…

A: Introduction: The Euler's method is a basic and numerical method to approximate an initial value…

Q: Let y(t) be the solution of dy/dt= 0.3y(2 − y) with y(0) = 1. Determine lim t→∞y(t) without solving…

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Q: If f '(1)=4, f(1)=2, and g(x)= f(x)·tan¬(x), what is the slope of the tangent line to the curve…

A: We can solve the problem by obtaining the tangent by doing derivative of the function given.

Q: Find the derivative of y with respect to t at t=2 if a) у %3D х + sinх - cos(1 + x+x?) аnd x = (t/t…

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Q: Evaluate lim X→0+ dx d sin ť dt . t O a) 1 O b) 1 c) 0 d) None of these e) H/2 5/2

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Q: Let f'(z) = tangent line to the graph of the function h(z) = g(13x+3) at e and g(x) = f(/#). Let L…

A: Given, f'x = ex2  gx = fx L is the slope of the tangent line to the graph of function hx = g13x+3 at…

Q: Find the tangent to y = cos x at x = 5- O A. y=x+7 O B. y= -x+7 O C. y= -x-7 O D. y= 1

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Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: We will use chain rule of partial derivative  If F is a function of  two independent variables x and…

Q: (d) Suppose that y(x) is a function and that y(2) = 1. Let y² + y = x. Using implicit differentian…

A: y2+y=x  Differentiating both sides with respect to x  ddxy2+y=ddxx    2y+1y'=1    y'=12y+1

Q: 16. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is 3π 2 A.…

A: This is a basic application of derivative problem

Q: 2. Evaluate dy and Ay if x = 1 and dx = Ax = 1. 3. Find the equation of the tangent line at x = 1.

A: Your question contain only two which i have solved completely.

Q: Find the linear approximation of the given function at (0, 0). f(x,y) = sqrt(y+(cos(x))^2)

A: The given function fx, y=y+cos2x The linear approximation in 2 variables is given by Lx, y-fa,…

Q: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

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Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: The tangent line to the curve y=f(x) is horizontal at where X = Xo f f(xx) = 00 A O f(xo) = 00 .8 O…

A: The tangent line to the curve y=f(x) is horizontal at where x=x0 if

Q: 6. Find all values of x in the interval [0, 2 n] for which the slope of the tangent to y e* csc(x)…

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Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: 1 sint j+e3t t valuate lim t0 2t +5

A: Given: The limit is limt→0 12t+5 i + sin tt j + e3t k .

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = 4

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Q: 1) Find the Linearization x of the function -V1+2x when x is near 0 Find the equation of the tangent…

A: As per Bartleby guideline if more than one question is asked only first question to be answered…

Q: Find In(y') at the point (0, 1/e) where xy° – In(xª + y) = 1.

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Q: 1. Consider the following function: y = f(x) = ln (2x² + 6x + 5) , for x > 0 (a) Calculate f'(0),…

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Q: Suppose that y is a differentiable function of x and w = cos(y5). Express the derivative of w with…

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Q: Find an equation for the tangent line to the graph of f(x) = -2x2 + 2x + 3 at the point where x = 1…

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Q: Suppose f( – 1) = 2 , f'( – 1) = 3 , and g(x) = r'f(x). The tangent line to g(x) at z 1 is given by…

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: Let T= f(x,y) be the temperature at the point (x, y) on the circle and suppose that on the circle x…

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Q: Let f(x,y) = 8x + 10y with x(t) = cos t, and y(t) = sin t. Find the derivative of w = f(x,y) with…

A: Here we have to find the derivative of w with respect to t.

Q: (d) Suppose that y(x) is a function and that y(2) = 1. Let y² + y = x. Using implicit differentian…

A: The objective is to find y'(2)and find the equation of tangent line to y(x) at x=2.

Q: 1. Consider the following function: y = f(x) = ln (2x² + 6x + 5) , for x >0 %3D (a) Calculate f'(0),…

A: GIVEN: y = f(x) = ln (2x2 + 6x + 5), for x≥0

Q: Find the equilibria of the difference equation xt+1 = stable or unstable. If xo = 1/2 what is lim x?…

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Q: If the Tangent line to y=f(x) at (1,2t pass through the point (0,3) Find l1) and f'(1) A. (1) = 0…

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Q: Suppose z is a differentiable function of x and y implicitly defined by the equation E : 2³ + xe² =…

A: Given function z3+xez=2-y3+lny3 cos(y+1)

Q: (2) Find the derivative of the following: In xy = e*+y 4. %3D y = esint (In t² + 1) 5. y = In e 1+e…

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Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Wr have to find the derivative of the given function first.

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Equation of tangent line through A(x1 , y1) is given by :- y – y1 = slope x (x – x1)

Q: 18. The equation of the tangent line to 2² sin T # 0 f(x) = 0 x = 0 at r = 0 is 1 (a) y = -x (b) y =…

A: Note:Since you have asked  multiple questions ,we will solve first question for you.To get remaining…

Q: Given that x'+3xy-y' = 6. Compute dy in terms of x and y by using implicit dx (c) differentiation.

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