sin πx , x< 2; Let f(x) = { sgn(a² + 2a – 3) , x = 2; cos , x > 2. 4 If the function f(x) is continuous at the point x= 0. then what is the sum of integers a ?

Q: Evaluate 5⁰⁰ x dx. -∞ x sin 2x x²+3 0

A:

Q: Find the sine transform of a function of x which is equal to sin x for 0 <x<a and 0 for x2a.

A:

Q: Use the product rule to differentiate the function h, where a and b are real numbers. h(x) = e¯ax…

A: According to product rule, if f(x)=u(x)*v*x) then f’(x)=u(x)*v’(x)+v(x)*u(x).

Q: | (cos c+ 1) dc;let x be constant

A:

Q: I-Shinx dx Ig-/sin'xdx 2-x2 dx

A: We have to evaluate the above integrals. NOTE - According to our guidelines we have to answer only…

Q: Evaluate L{t°e! e3(1 – t) 3e-t sin (4t - 2) 2) + t2 $ (3t)} cos

A: Explanation of the answer is as follows

Q: -1x) dx

A:

Q: Determine whether the given set of functions is linearly independent on the interval (-co, co).…

A:

Q: Evaluate sec³ (0) tan³ (0)dē. ○ sec (0) - sec³ (0) + C ○ sec³ (0) + sec³ (0) + C O sec³ (0) + sec(0)…

A: Step 1:To solve the integral ∫sec5(θ)tan3(θ)dθ, we can use substitution and trigonometric…

Q: Evaluate D³(sinx - 4e²x) A -sin x-32e²x B -cos x-32e²x (C) с cos x-32e²x D sin x-32e²x

A:

Q: 3. (a) Let f(t) = t – sin t for all t. Show that f is a strictly increasing function of t, and…

A: f(t) = t - sint for all t  So, f'(t) = 1 - cost for all t  &amp;, f"(t) = sint for all t

Q: What is the range of f(r) = cos(x)? i) [–1, 1] ii) [0, 1] iii) (-∞, ∞) O i O i

A:

Q: Find all xE[0,2pi] that satisfy sin 2x + cos x = 0 x =

A: Topic- Trigonometric Equations We are given, sin(2x)+cos(x)=0 and x∈[0,2π] We know that sin(2x)=2sin…

Q: Evaluate: f(cos 5x - 2 sin 3x) dx O sin 5x - cos 3x + C Osin 5x - cos 3x + C O sin 5x+cos 3x + C…

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Q: Find the analystic function f(z)u+iv if u=a(1+cos0)

A:

Q: sin(2x) = - 1/2 for 0 ≤ x ≤ 2pi

A: Given query is to find the solution for the x.

Q: 3T/2 1|sin(x| dx 01

A: Topic = Integration   using this definationsin x=sin xif 0≤x≤π-sin xif π&lt;x≤2π

Q: Let a be a constant. Evaluate 2 ((2* + 2² + a) sin(4x³) + 12a²)dx.

A:

Q: Let f(x) = 7 sin(x +7)+ cos 2x. Compute f(13) (0).

A:

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.