In Rolle's theorem ,If f(x) = tanx be a real valued function in [0, r],then theorem %3D A. exist B. not exist C. 0 D. I Select one

Q: Consider f(x) = x + sin(x) on the interval [0, 27]. %3D

A: Find y intercept. Increasing/Dercreaing, critical point

Q: Determine the values of a, b, and c so that the function (sin(a + 1)x + sin x x0 is continuous for…

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Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: Let f(x) = cos (x). %3D If it is true that f" (x) = x(f'(x))ª for some constant a, find the value of…

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Q: 4. How many fixed points does the function T(x) = tan(x) have? %3D

A: for fixed point f(x) = x x = tan(x)

Q: Let f(x)  = tan x . Show that  f(0)  = f(π)   but there is nonumber c  in  (0, π)such that f'(c )…

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Q: Find f(x), where f'(x) = sin(x)+ cos(x) + 1 and f(r) = 2. %3D %3D

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Q: What is the rule of a function of the form f (a) = a sin(br +c) +d or f (x) = a cos(br + c) +d whose…

A: We are asked to find the equation of the graph.

Q: (tan ) 1/x TC + x 4 * f(x)D. k, For what value of k, f (x) is x =0 continuous at x = 0?

A: The

Q: (a) integrate to find F as a function of x, and (b) demonstrate the Second Fundamental Theorem of…

A: ∫π3x sect tant dt

Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(T/4) = 5? %3D

A: Given: f(x)=cx+log(cos(x))  and f'π4=5 find values c

Q: Use the Fundamental Theorem to show that the following are true.

A: Recall the Fundamental theorem of calculus that ∫abfxdx=Fb-Fa.

Q: (2n )! | [P, (x)]° dx | (1-x?)" dx %3D 22" (n!)2 -1

A: Solution

Q: Let f(x) = (c + 1)x+ In(cos x). For what value of c is f'(/4)=6

A: This question can be solved using the concepts of differentiation.

Q: Find f(x), where f'(x) = sin(x) + cos(x) + 1 and f(#)=2. %3D %3D

A: Using anti derivative formula.

Q: Find a function f and a real number a such that :| f(t) dt = x tan-r. + 4

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Q: Use the Fundamental Theorem of Calculus,Part 1, to find the function ƒ that satisfies the…

A: We have to use the fundamental theorem of Calculus Part-1 to find the function f that satisfies the…

Q: Find a function f and a real number a such that 4 + | f(t) dt = x tan -1 x. -

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Q: State the domain on which the function is continuous. h(x) =(cos(1/x))/(x2−1)

A: Domain is defined as the set of all points over which a function is defined.

Q: Consider the following. F(x) = dt (a) Integrate to find F as a function of x. F(x) = (b) Demonstrate…

A: Second fundamental theorem : Suppose f is continuous function in an open interval I .Let a∈I and a…

Q: Let f(x)= sin X, - SXS g(x) cos x, 0sxsn, and h(x) tan x, 2 Find the exact value of the composite…

A: We are asked to find the composition function

Q: We can not find an analytic function f=u+vi such that 3u-v is not harmonic. * True False

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Q: Evaluate | F • dr where F (0, y, – 4x), and C' is given by - F(t) = (t, sin(t), cos(t)), 0 <t<

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Q: (a) integrate to find F as a function of x, and (b) demonstrate the Second Fundamental Theorem of…

A: Solution; (a) Consider the given integral is: F(x) = ∫π4xsec2 t dt Since we have ; ∫sec2 x dx = tan…

Q: Let f(x) = tan x. (a) Find the linearization of f(x) at x = (π)/(4).…

A: Given that the function: fx=tanx…

Q: Consider the function w = f(x,y), where %3D x = r cos 0 and Y = r sin 0 Verify each of the…

A: To find the function in terms of x and y, use the trigonometric identity, cos2x+sin2x=1 and…

Q: Find ao of the function f(x) 1-Cosx f(x) =

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Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(n/4) = 9?

A: f (x) = cx + ln ( cosx)To Find: For what values of c is f' (π4) = 9Proof: We will differentiate f(x)…

Q: Let f(x) = w when 0 < x < a and 0 otherw 00 w sin ak cos()dk =

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Q: 12. Let f(x, y) = tan(ry). Find f, and fy for this function.

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Q: Express the function in the form  f ° g   F(x ) = cos x2

A: Given that, F(x) = cos (x^2) Let us consider, f(x) = cos x g(x) = x^2

Q: Describe the interval(s) on which the function is continuous. f(x) = cos 1/x

A: Given- fx=cos1x To find- The intervals on which the function is continuous. Concept Used- As we know…

Q: Let f(x) : number c in (0, 7) such that f'(c) = 0. Why does this not contradict Rolle's Theorem? =…

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Q: If f: R R and g: R R be functions defined by f(x) =x + 1 and g(x) sin x %3D %3D

A: Introduction :

Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: Let f(x) = e cosx, sx %3D 2. Express your answers in exact form. ElN

A: Inflection point occurs when the second derivative of the function equals to zero.

Q: Prove that the identity function is differentiable at every x E R

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Q: Find the local extrema of the function f(x)=x+cos2x.

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Q: Prove that the function f(z) = sin(x)cosh(y) + i cos(x)sinh(y) is entire.

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Q: Q2. Let f(x) - In(cos x) (i) Find the are length (ds) of the function

A: Given,                f(x) = ln(cos x) ⇒y=ln(cos x) ⇒ dydx=-sin(x)cos(x). And we have to find arc…

Q: Let f(x) = cx + In(cos(x)). For what value of c is f' = 4? %3D 4 C =

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Q: The function f(x) sin x + cos x is an even function. True False

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Q: Find the linearization of the following functions at x=0. a) sin x L(x)= x b) cos x L(x)= 1 c) tan x…

A: As per guideline we have to solve only three

Q: A function f is defined by f (x1) = / Cos(x – t) os(x-t) dt cos(t) f (x) : 01 Simplify f(x) and…

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Q: a) Find the linearization of the function f(x) = cos(x) at a = π/2, b) Use a) to approximate…

A: (a) We have,

Q: 0 to π produce an invertible function for the function f(x) = cos x? Explain.

A: Inverse of a function

Q: In(x) Differentiate the function F(x) | cos(e') dt (for x>0). %3D 1/r Show and justify your work.

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Q: Find a function f such that ∇f = ex cos yi − ex sin yj + zk.

A: Given, ∇f = ex cos yi − ex sin yj + zk.

Q: (2) Consider the functions f(0) = tan2(0) and g(0) = sec2(0). df (a) Compute de

A: Consider the functions fθ=tan2θ and gθ=sec2θ Here, the objective is to differentiate the function…

Q: Is there a value of c that will make sin² 3x f(x) = C, x = 0 continuous at x = 0? Give reasons for…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.