Q 4 Sketch the graph of a function that satisfies all of the given conditions: f'(x) < 0 Vx, limrtoo(f (x) + x) = 0, f" (x) < 0 if lal< 1, f" (x)> 0 if lal> 1

Q: A curve, y=f(x) passes through the point (1, −1)(1, −1) and the slope of the tangent at any x is…

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Q: 4. 1. Let f(x) = (sinx)*tan(1 – x)e30x. Find the maximum of f(x) in [0,1] and ɛ = 0.05. (by handly…

A: Given: fx=sinx6tan1-xe30x. We have to find the maximum of fx in 0,1.

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx² + 5 at =2 ? B) Find the limits by…

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Q: Find all points (if any) of horizontal and vertical tangency to the curve on the given interval

A: Given Data The first equation is x=cos θ+ θ sin θ. The second equation is y=sin θ- θ cos θ.…

Q: 5a) Using the formula man = lim+)=/G2 determine the derivative/ slope of tangent for h→0 the given…

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Q: 2. Find all x values on the graph of f (x) where the tangent line is horizontal for each of the…

A: To find: The values of x on the graph f(x) where the tangent line is horizontal. Given information:…

Q: 4 4) (i) Find the equation of the tangent line at the point (2, 4) for the curve, f(x) = x². (ii)…

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Q: Please use Limits this is under calculus section

A: When x = 2, y = g(x) = 4 / (x - 1) = 4 / (2 - 1) = 4Hence, the point of tangency is (2, 4)

Q: Find the absolute maximum and minimum values for f(x, y) = 5 sin(x) + 10 cos(y) on the rectangle R…

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Q: 3.44 3. Test for homogeneity f (x, y) tanx-sec²x - cosy

A: Question : Test for the homogeneity f(x, y) = tanx - sec²x - cosy

Q: Find the extreme values of the function f on the interval [0, 7), and the z-value(s) at which they…

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Q: 1. How do I solve this?     2. How would I find the tangent line to the graph at x=-1

A: Consider the given function.

Q: 3. i. Find f'(x) if f(x) = 9² + tan='(x²) + In(x® + 2x) + cos I +5*. dy ii. Find dr² at the point…

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Q: Find a tight upper bound for the approximation to * cos(z) cos(x) Note that the second derivative of…

A: Concept: Midpoint rule: Assume f(x) is a continuous function on [a,b]. Let n be a positive integer…

Q: 7. Suppose the equation əz ar is a differentiable function of r and y implicitly defined by 2³ = y²…

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Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given         f(x)=sin-1x , a=π12

Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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Q: 73 9x +4 then f(x) has a local maximum at the point 3 Use second derivative test, If f(x) %3D - O…

A: Topic:- application of derivatives

Q: 5. Find the exact absolute maximum and absolute minimum values for f(x) cos(x) + sin (x) on the…

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Q: 4. 1. Let f (x) = (sinx)ʻtan(1 – x)e30x. Find the maximum of f(x) in [0,1] and & = 0.05. (by handly…

A: We will use Newton's method of optimization to find the maximum value of f(x)

Q: 1 The equations of the vertical asymptotes of the function with rule f (0) = are: 1+ cose

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Q: The function (f) with a period of 2π is defined by: f(x) = cosh (x - 2π)  if x∈[π ; 3π] a) Using…

A: We have to graph the function f(x) on the given interval.

Q: Suppose that g is a function with second derivative g"(x)=sin(e2 – 1). It is also known that g'(1)=0…

A: Given that: g''(x)=sin(ex-1)g'(1)=0

Q: Find the extreme values of the function f on the interval 0, 7, and the x-value(s) at which they…

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Q: 7. Use the limit definition of the derivative to find f'(r). Then find the equation of the tangent…

A: Solution is given below:

Q: 3. Find the absolute maximum and the absolute minimum of f(x) = x-2 tanx on the interval [0,4].

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Q: A quadratic function f(x) = x + 3 x2 + 2 x + 3 has an inflectional tangent y = 3 x + 3 at (0,0).…

A: Given:- A quadratic function f(x) = x3+3x2+2x + 3 has an inflectional tangent y = 3x + 3 at (0, 0).…

Q: 5. Find the length of the curve x =y? +2} from y =0 to y = 3. In(5x+2). In 3x 6. Solve lim

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Q: 20 Let f(x) = 4x + x2 given by y = mx + b for . Then the equation of the tangent line to the graph…

A: We have to find

Q: 4. Find the absolute maximum and absolute minimum of the function f(x) = 3 sin(x) cos(x) over the…

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Q: Please show step-by-step solutions.

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Q: 6. Find the values of at which the graph of f(x) = = 4x² - 3x + 2 has a tangent line parallel to the…

A: Follow the procedure given below.

Q: 13.Find a sinusoidal function with a maximum value of 9 that occurs at x=4 , and a minimum value of…

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Q: 2 2x +1 Let f(x) =- |- log, (x² + + 1) • (b* - 5b +3)x +c. If f(x)isa tan decreasing function of x…

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Q: Question 3 Consider a differentiable function g with domain [0, 0). Given that g'(x) = a e" and…

A: If g'' is negative then x is point of maxima if g'' is positive then x is point of minima

Q: 10. Consider the function f(x, y) = 4 + x* + 3y* a. Show that the Second Derivative Test is…

A: (a) Calculate the value for second partial derivatives w.r.t x and y.…

Q: 2. Let f (x) = 5x2 –7. (a) Use the definition of the derivative, f'(a)= lim s(a+h}- f(@) %3D A-40 to…

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Q: Proove: Yn- n-1 x

A: Given That : Let us assume that  y=xnlog(x) Prove that : yn=n!x using Leibnitz  theorem

Q: 1-cos (x-T) lim x→T(x-T)sin (x-π)

A: Given limit, limx→π1-cosx-πx-πsinx-π

Q: 6) Determine an equation for a quintic function with zeros -1 (order 3) and 3 (order 2) that passes…

A: In this question, concept of polynomial is applied. Polynomial The term "polynomial" refers to a…

Q: 1. Find all the local and global extrema of the function f (x) = sin(x) – x [-27, 27]. Clearly…

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Q: 1 and y = g(æ) has a 1, then the graph of y = f(x)g(x) has a horizontal tangent line at ) and g(x)…

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Q: 15. Find any local maximum and local minimum values , then sketch each curve by using first…

A: We use first derivative test to find local maximum and minimum

Q: 15. Find any local maximum and local minimum values , then sketch each curve by using first…

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Q: 2. (a) Demonstrate the method of the limit definition of derivative to find the derivative of f(x) =…

A: Limit of differentiation

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx² + 5 at =2 ? B) Find the limits by…

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Q: Q.NO.2: i. Find the limit Зх — sin(kx) lim - k + 0 ii. Find the relative extrema using both first…

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Q: 1) Suppose the second derivative of a contiovous function given by f"(x)=Cx-2 )3 (x-2)2 (sx-) A…

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